Recent content by frostshoxx

Can this be done symbolically? Also, what do you mean by contradiction? could you give some examples? Thank you for your time.

Homework Statement Prove that every square real matrix X can be written in a unique way as the sum of a symmetric matrix A and a skew-symmetric matrix B. Homework Equations X = A + B A = \frac{X+X^{T}}{2} B = \frac{X-X^{T}}{2} X = \frac{X+X^{T}}{2} + \frac{X-X^{T}}{2} The...

Since we know that both a and b must be positive value Therefore, if we take square root on both side of equation (a^2) > (b^2). it would make a > b always. Would this work?

Oh my mistake... so anyway, that would make Transpose (Transpose(B) * S * B) = Transpose(B) *Transpose(S) * B, correct? How would this lead to the proof that Transpose(B) * S * B is a skew-symmetric matrix for S is a symmetric matrix and B is any square real-valued matrix?

Thank you for the quick post. Tranpose (AB) = Transpose(A) * Transpose(B) for any A and Bmatrices. Transpose( Transpose(B) * S * B) = B * Transpose(S) * Transpose(B). Am I correct? What would be the next step to approach the end goal?

Homework Statement Hi, I need to prove that if S is a skew-symmetric matrix with NXN dimension and B is any square real-valued matrix, therefore the product of transpose(B), S, and B is also askew symmetric matrix Homework Equations This is what I know so far. 1.Transpose(S) = -S...