ShmoopTube

00:04

Identity Matrices, a la Shmoop.

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Jason Borneo can’t remember anything important about his life… [Man with a bandage on his head]

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…his name, his address, his iTunes password… nothing. [Man holds up a name badge with a qeustion mark on it]

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All he has in his possession is a briefcase containing a matrix. [Man opens a briefcase that has a note in it]

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And a banana, but he’s saving that for later. [Banana appears in the briefcase]

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To learn his identity, Jason must create an identity matrix that corresponds to the matrix

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in his briefcase…

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…and multiply them together.

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The original matrix is 2 rows by 3 columns, with values 2, 9, 34, -90, 32, 1.

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An identity matrix is a square matrix whose diagonal is composed of ones.

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The remaining values of the matrix are zeroes.

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In order to find the dimensions of the identity matrix that correspond to the original matrix… [Matrix written out next to a matrix with a question mark]

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…Jason just has to look at the number of columns of the original matrix.

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For his 2 by 3 matrix, the corresponding identity matrix would be 3 by 3.

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Now he can multiply the two using the standard procedure of matrices multiplication:

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2 times 1, plus 9 times 0, plus 34 times 0 is 2…

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…2 times 0, plus 9 times 1, plus 34 times 0 is 9… [Arm pointing to the numbers which are being multiplied]

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…2 times 0, plus 9 times 0, plus 34 times 1 is 34… and so on with the second row.

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The end result when multiplying by any identity matrix is always the original matrix.

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We can think of an identity matrix as the matrix equivalent of “1.” [The original matrix next to the identity matrix]

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Upon completion of Jason’s mission… [Man with a bandage on his head with his thumbs up]

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…a second, smaller briefcase unlocks, containing all of his personal information. [A smaller briefcase inside the original briefcase with a pile of documents]

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It turns out he’s a stockbroker living in Pittsburgh. [The man looks surpised]

01:53

Hm.

01:54

Kind of anti-climactic. [Man looks upset and cries]

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