I have no idea where to start to prove this.

Let where is the identity, is a non-zero row vector in and denotes transpose of . If is symmetric, show that .

both symmetric, then of course is symmetrc. But how to show is equal to identity?

Printable View

- Mar 30th 2010, 01:30 AMdeniselim17linear algebra proof
I have no idea where to start to prove this.

Let where is the identity, is a non-zero row vector in and denotes transpose of . If is symmetric, show that .

both symmetric, then of course is symmetrc. But how to show is equal to identity? - Mar 30th 2010, 04:40 AMtonio

Without any further conditions this is false: take for example , then:

, so is symmetric but is not the unit matrix.

As you say: sum/difference and product of symmetric matrices is symmetric, so the above difference will**always**be a symmetric matrix, no matter what is.

Tonio - Mar 30th 2010, 05:47 PMdeniselim17
- Mar 30th 2010, 06:52 PMtonio