Question

If A is symmetric, every eigenvalue of A is non-negative if and only if
(a) A = A² is orthonormal
(b) A=B² for some matrix B
(c) A=B² for some symmetric matrix B
(d) A²=B² for some symmetric matrix B​

Answer 1

Answer:

Symmetric B can be rewritten as SΛS−1 since symmetric matrices are always diagonalizable. So, B2=SΛS−1SΛS−1=SΛ2S−1

Therefore, all the eigenvalues are squares of real numbers(property of symmetric matrices), so the eigenvalues are all positive.

Answer 2

Answer:

third asymmetric-key very equal and when a value is equal to 8 available from matrix sum of symmetric matrix