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Hi guys, I'm gonna give you a quick[br]crash course tutorial on MathLab for

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first timers or[br]approximately first timers.

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When you first open MathLab you're[br]gonna see stuff like these,

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get rid of these as soon as you can,[br]that's just getting in the way.

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You can still use them, they're[br]still there, you just have to hover.

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This is the command window.

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You can use it like a calculator.

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Do all of your code immediately,[br]and get response back.

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I like to open up a script, and open[br]up the editor so I can write a script.

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And it's really clean in here.

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And then you can evaluate,[br]over in the command line.

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Notice, they're right next to each other.

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You can see.

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All the code heightwise.

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You can actually do this as well,[br]minimize the tool strip if you wanted to.

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I've already got a file here[br]that we're gonna run through.

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And then go through all of[br]this as quickly as possible.

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So just pause, rewind if you have to.

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When you start evaluating code in[br]the editor, you can set these break points

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here to evaluate up to that point,[br]and then you can continue stepping.

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You can also set modify condition,[br]so this is a Boolean condition here.

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So to run, I like to use hotkeys.

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This is function F5, to run.

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Or you can just use one of the arrows,[br]up here, when there's a run arrow.

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Anyway, so[br]now that it's running in debug mode,

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I can continue stepping by clicking[br]this or just use the hotkey.

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So this first line, I stored a row vector,

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an array in a row into x1.

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And it goes from minus 2 pi to 2 pi.

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Or at least it's supposed to[br]go from minus 2 pi to 2 pi.

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It defaults,[br]when it's just one colon there,

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it defaults to integer value increment.

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So you see over here it went[br]from -2 pi but it didn't quite

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hit positive 2 pi because[br]the incrementation didn't allow it.

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So the next line here allows[br]it to do that because I

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enforced the conditions that it[br]reaches a total range of 4 pi.

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And it reaches that over 13 increments,[br]so there was a total of 14 points.

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And if you look at here, X2,[br]it goes from minus 2 pi to 2 pi.

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And he's our way to do this without[br]having to think about how to increment,

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is just to use the linspace command.

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And you just tell it how[br]many points you want.

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This one, in this case, it's 14 points[br]that it's identical to this, x2 and

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x3 are identical, if you look over here,[br]they're identical.

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Just easier to use lens space sometimes.

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There's also log space.

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I created lens space again,[br]and using these for later.

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100 points for log spacing.

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This log space gives me ten to[br]the zero to ten to the six.

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So it goes from one to a million[br]over a hundred points.

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So if you see, you look over here,

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this is the very largest number,

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it's a 1 times 10 to the sixth,[br]it's a million.

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Here's a matrix.

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It's a this is the first row,[br]second row, and they're separated,

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rows are separated by a semi colon.

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This a row vector B,[br]this is a column vector C.

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The same values just one is[br]a transpose of the other.

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It was three by four matrix of zeros,[br]three rows, four columns.

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Matrix of ones,[br]three by three identity matrix.

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Now, when we started[br]doing matrix operations,

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let's take a look at how to solve this,[br]A times Y is equal to B.

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If we know A and we know B,[br]how do we solve for Y?

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So we invert A, so[br]I'm gonna grab this and put it down here.

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This operator says,[br]invert A and operate on B.

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This is going to give me an error because[br]the matrix dimensions must agree,

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which means MathLab doesn't know how[br]to operate a matrix on a row vector.

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So this row vector for the least,

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the less obscure mathematical operation,[br]which is just matrix

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multiplication that has to be a column[br]vector, it has to be a column vector.

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There's also a way to do a row[br]vector here but it's a more

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obscure operation,[br]out of product of some sort.

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MathLab doesn't know how to[br]do it unless you massage it.

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So you come over here and you put this[br]transpose operator, this tick mark, and

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that'll allow it to do[br]the correct operation.

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So that gives me a solution.

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My solution Y for this linear system.

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And then YY is gonna be the same thing[br]because C is already the transpose of B.

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[COUGH][br]This is to check to make sure that I get

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B back, so there's B back.

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When I got my solution Y.

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Now here if I have an array of[br]input values into this function,

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then this function automatically[br]loops through all those values, so

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you don't have to write[br]your own four loop.

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So that's the output here is the sign[br]of every one of those individually.

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Now I'm gonna use these down below here.

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So this dot here

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doesn't mean dot product it means[br]element wise multiplication or

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in this case element wise multiplication,[br]down here it's element wise division.

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So it just takes the first element here[br]multiply it with the first element here.

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Second element here, multiply it by[br]the second element here, and so forth.

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And stores it in W.

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So if you look at the size of w, compare[br]it with the size of either Y1 or Y2,

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it doesn't matter,[br]they're both the same size.

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And size returns all dimensions.

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As compared to length which I[br]have suppressed the output so

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I have to actually bring it over.

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Let's say for example, length of B,[br]B if you look up here,

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B is 3 by 4 and C is 4 by 3.

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So the length of either of these

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is the same because length[br]finds the longest dimension.

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So going into the plotting,

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you can just call up the plot function and[br]it brings up a figure.

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Applies to that figure, you can come in[br]here and insert labels, title, legend and

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all the stuff right here[br]if you wanted to but

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I suggest since we're gonna be coding[br]a lot just get used to writing your code

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to do everything for[br]you at least as much as possible.

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So there we added a title to it,[br]we added a label.

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Now if I wanna add another[br]plot to the same figure

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I have to hold on to the figure.

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[COUGH] So then I can throw in another[br]plot under that same set of axis,

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let go the figure.

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Just because I've let go of it,[br]you might assume that you can now

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start another plot and it'll create a new[br]figure for that plot, but it doesn't.

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It overwrites on top of this,[br]it writes to the same figure.

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So that's an obvious problem,[br]the way to get over that is by explicitly

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calling the figure,[br]this is just a quirkyness with MathLab,

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there's probably a way around it,[br]I just, I'm not aware of it.

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So create a whole new figure,[br]and then plot to that.

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So it's the same thing with subplot.

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If I just start subplotting, it's gonna[br]write over the top of this figure.

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Then it's gonna create a subplot axis or[br]set of axis and

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then it's gonna plot to that set of axis[br]and it's gonna tie it all to that axis.

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Now this X label, notice how I've[br]done this, it's a carrot for

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a super script and[br]then an underscore for a subscript.

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And the curly braces are if you have[br]multiple characters that you need to

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include in the scripts,[br]in the subscripts, super script.

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So then the subplot it says[br]make me a 2 by 1 region

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and here is populate in[br]the first region and

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now it's populating in the second region,[br]these plots.

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So there's the second region of the plot,[br]title, label, okay?

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So if I continue going now since[br]I have called figure again,

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this is going to override this and that's[br]fine because I'm done looking at all this.

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Well okay, so notice that it[br]didn't override the whole thing,

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it just overwrites the current axis.

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So this is an exponential.

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We have a linear set of[br]points on the input and

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then we have the exponential[br]set of the output.

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I want to get rid of,[br]I want to look at this on,

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let's call our new figure, whoops.

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So now I can look at both of these[br]if I choose to at the same time.

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So notice how I have.

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Just gone from plot to send their log Y.

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So it suppress the exponential[br]growth in the Y direction by scaling

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it logarithmically.

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Now, if I give inputs that[br]are growing exponential and

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then the output is exponential[br]of the exponential input.

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It wants to be a double[br]exponential growth.

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So let's see what that looks like.

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Well, the problem here, you won't be[br]able to see it, unless we plot it.

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That's a straight line,[br]notice the X-axis here

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doesn't come any where near[br]the largest X values of X log.

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Remember this is,[br]one million is the largest value.

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So what's happened is it's gone to[br]the maximum that this can possibly go to,

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on the Y value.

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That's the maximum it can go to, before it[br]thinks that all the numbers are infinity.

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So this actually goes infinitely higher,[br]and this goes much further to the right.

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So this is a totally garbage,[br]a total garbage plot here.

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It doesn't, it's meaningless.

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So I'm gonna rescale, I'm gonna create

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X log small enough that it'll[br]actually plot those values.

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So now you can see,[br]I should probably get rid of these dots.

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Let's replot this new set of points.

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Just a default solid line.

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So this is,[br]this actually is the exponential growth

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of the inputs and it goes over all[br]possible values of the inputs.

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So that's still not very[br]appealing to look at so

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let's create a new figure and[br]suppress the logarithmic or

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the exponential growth in the X-axis now.

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So we we semi log X and[br]notice that I don't have

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to repause a million times,[br]but let's do this.

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So it is an exponential growth, it's[br]doubled the exponential because the input

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is, the inputs are growing exponentially[br]and the output is growing exponentially.

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It's tough to see it's exponential because[br]there, it's doubled the exponential.

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So if you have a doubly[br]exponential growth,

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the input and the output then do log log.

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And that shows you[br]the exponential characteristic.

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All right, that's about it for this video.

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The next one will go into more depth.