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These are the user uploaded subtitles that are being translated: 1 00:00:00,390 --> 00:00:05,910 Hello everyone and welcome to lecture on matrix arithmetic in this lecture we're going to be discussing 2 00:00:05,910 --> 00:00:10,080 just basic arithmetic and some basic operations on a matrix. 3 00:00:10,080 --> 00:00:11,620 Let's go ahead and jump to our studio. 4 00:00:11,640 --> 00:00:13,470 See how this all works. 5 00:00:13,470 --> 00:00:18,310 All right so here we are our studio when I'm going to go ahead and do is create a matrix. 6 00:00:18,320 --> 00:00:20,730 Just go ahead and call it Matt. 7 00:00:20,760 --> 00:00:21,890 Keep it simple. 8 00:00:22,050 --> 00:00:28,830 I'll use the matrix function or go him Pessin a vector using that colon rotation because it's just a 9 00:00:28,830 --> 00:00:30,720 sequential series of numbers. 10 00:00:30,720 --> 00:00:37,000 Let's go ahead and say by RHO is equal to true the capital-T is fine. 11 00:00:37,100 --> 00:00:43,020 Now I will specify the number of rows using end row argument parameter as 5. 12 00:00:43,320 --> 00:00:49,060 So this should result in a five by five matrix of the numbers 1 through 25. 13 00:00:49,250 --> 00:00:54,150 Now just walk through just some simple arithmetic operations just like a vector. 14 00:00:54,180 --> 00:00:59,490 If you do arithmetic operations with a scalar so a single number everything is going to be done on an 15 00:00:59,490 --> 00:01:01,200 element by element basis. 16 00:01:01,200 --> 00:01:08,200 So if I wanted to multiply all the numbers in my matrix by two I would just do Matt Asterix too. 17 00:01:08,250 --> 00:01:13,470 So I wanted to divide everything by two would just be a single slash divided by two. 18 00:01:13,940 --> 00:01:16,890 So I want to do everything in the power of two. 19 00:01:16,980 --> 00:01:18,810 I would just say that little carrot symbol. 20 00:01:18,810 --> 00:01:20,280 That's the power of two. 21 00:01:20,370 --> 00:01:26,130 I can even do reciprocals in the same manner so I can say 1 divided by Matt which is going to be the 22 00:01:26,130 --> 00:01:32,640 same as the basic reciprocal of every single element in that matrix. 23 00:01:32,640 --> 00:01:33,250 OK. 24 00:01:33,400 --> 00:01:37,230 So hopefully this looks pretty familiar given what we learn about vectors. 25 00:01:37,320 --> 00:01:42,810 We can also use comparison operators of matrices just like we could with vectors and remember with vectors 26 00:01:43,020 --> 00:01:45,780 we got in return an entire vector of logicals. 27 00:01:45,870 --> 00:01:50,550 In this case we'll get in return an entire matrix of logicals. 28 00:01:50,550 --> 00:01:57,630 So if I wanted to grab let's say everywhere where the matrix was greater than 15 I could do this and 29 00:01:57,630 --> 00:02:05,370 then I would get in return a matrix full of logical values and just like with the vectors I can use 30 00:02:05,370 --> 00:02:10,140 the same sort of notation actually filtered out by those values. 31 00:02:10,140 --> 00:02:14,470 So that's going to return a vector of where of all the values were that was true. 32 00:02:14,870 --> 00:02:15,390 OK. 33 00:02:15,690 --> 00:02:22,740 So we can even use matrices in arithmetic operations with each other like an atom matrices together 34 00:02:22,740 --> 00:02:22,830 . 35 00:02:22,830 --> 00:02:27,830 So if I wanted to say map plus map that's going to be the same as MAP times to. 36 00:02:27,930 --> 00:02:33,600 I can even do things like Map divided by map and that should all equal one which makes sense because 37 00:02:33,660 --> 00:02:36,570 any number divided by itself is equal to 1. 38 00:02:36,570 --> 00:02:39,310 So hopefully this all looks again pretty familiar. 39 00:02:39,490 --> 00:02:46,050 You can even do powers so I can say map to the power of map that's going to be some really large numbers 40 00:02:46,050 --> 00:02:48,510 here which makes sense but it all works out. 41 00:02:48,990 --> 00:02:57,070 And I can do let's say Matt Times Matt to go ahead and say 1 times 1 2 times 2 3 times 3 etc.. 42 00:02:57,180 --> 00:03:00,160 Now a quick side note on Matrix multiplications. 43 00:03:00,240 --> 00:03:06,480 If you're familiar with linear algebra you'll notice that this isn't actually true matrix multiplication 44 00:03:06,480 --> 00:03:06,930 . 45 00:03:06,930 --> 00:03:11,190 So if you're familiar with the mathematics behind this topic then you would actually like to use are 46 00:03:11,340 --> 00:03:13,930 to perform true matrix multiplication. 47 00:03:13,950 --> 00:03:16,680 You can check out the Wikipedia links provided in the notes. 48 00:03:16,680 --> 00:03:23,400 For more background on matrix multiplication you can actually just use the following syntax so go ahead 49 00:03:23,400 --> 00:03:28,170 and make an example of this instead of saying. 50 00:03:28,180 --> 00:03:30,070 Matt times Matz. 51 00:03:30,240 --> 00:03:33,540 Which group would perform element by element multiplication. 52 00:03:33,540 --> 00:03:39,510 The action wanted to perform true matrix multiplication in the linear algebra concept of multiplication 53 00:03:39,510 --> 00:03:39,850 . 54 00:03:39,960 --> 00:03:45,870 You would use percentage signs surrounding that Asterix in order to confirm that you actually want to 55 00:03:45,870 --> 00:03:48,510 do matrix multiplication. 56 00:03:48,510 --> 00:03:50,370 So notice how those results are different. 57 00:03:50,430 --> 00:03:51,180 Don't worry too much. 58 00:03:51,210 --> 00:03:56,400 If you're not familiar with matrix multiplication in that linear algebra sense this is just for some 59 00:03:56,400 --> 00:04:00,550 quick information for those people that do know how to use that. 60 00:04:00,590 --> 00:04:02,840 OK so that's it for this lecture. 61 00:04:02,850 --> 00:04:07,470 It should all be feeling familiar because of everything we've gone over through vector's centrally. 62 00:04:07,470 --> 00:04:12,290 All the same operations the same indexing notation it's just in two dimensions. 63 00:04:12,320 --> 00:04:15,480 OK thanks everyone and I'll see at the next lecture. 6622