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...