00:01
In this video, we're considering a matrix a.
00:03
And what we have is that a is written down in this notation here, where a1 through a .n are the columns of a.
00:10
There's n columns, and we're going to assume that each column has m entries, so that overall, a is an m by n matrix.
00:19
Now what we're going to do next is consider this matrix, which is im.
00:26
This is going to be a square matrix of m rows and n columns, which is also the identity matrix.
00:32
That means we can write it in column form using this same kind of notation with e1, e2, up through e, m, as this way.
00:45
So this is our identity matrix, and recall if we pick any one of these columns, e1 just means we have a matrix, or excuse me, a vector, with m entries, and 1 will be in entry 1.
00:58
For this one, one is going to be in the last entry m, one will be in the second entry of this vector, and so on.
01:06
So what we're going to be doing next is multiplying the identity matrix i .m with our metrics a.
01:17
Let's write out what this would look like...
