00:01
We're told that b is a real non -singular matrix.
00:11
In part a, we're asked to show that the matrix b transpose b is symmetric.
00:19
Well, consider that the transpose of b transpose b transpose b, this is equal to, using laws of transposition, b transpose times the transpose of b transpose, and this is the same as b transpose times b.
00:45
And therefore, it follows the matrix b transpose b is symmetric.
00:59
Then in part b, we're asked to show that b transpose b is also positive definite.
01:07
Well, let you be a non -zero vector.
01:10
Then the inner product of u with b transpose b times u.
01:25
Well, this is the same as u transpose times b transpose b times u, which can also be written as u transpose times b transpose using associativity times b times u, which in turn this is b you transpose transpose.
01:51
Times b .u...