00:01
Okay, so for this problem, we consider the following matrix.
00:05
A transpose times a equals to 4 -0 -0.
00:11
So since this matrix is already a diagonal matrix, so it has two eigenvalues, lambda 1 equals to 4 and lambda 2 equals to 0.
00:23
According to this result, we have the singular values for a, sigma 1 equals to 2.
00:29
And with these singular values, we construct the matrix capital sigma equals to 2 ,000.
00:41
So the size of this matrix sigma is the same as the original matrix a.
00:49
And so we need to figure out the rest part for the singular value decomposition.
00:56
So lambda 1 equals to 4.
00:58
So a transpose a minus 4i equals to 0000.
01:05
So since it's a 0 matrix, so the eigenvector is kind of arbitrary.
01:13
So we can just simply choose v1 equals to 1 0.
01:18
For lambda 2 equals to 0, a transpose a minus 0 i equals to itself.
01:28
So we can simply choose another eigenvector for lambda 2...