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?
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?
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