How do I span a vector space of $4\times 4$ matrices with real values by symmetric and skew symmetric matrices?
The basis of vector space of $4\times 4$ matrices has 16 elements, each containing one 1 and fifteen 0's. All I have to figure out is finding a combination of symmetric and skew symmetric matrices to get each of these elements.
Please just provide a hint.
Thank you in advance.
Best Answer
Hint: For any square matrix $A$, one has $A = \frac{1}{2}(A+A^T) + \frac{1}{2}(A-A^T)$.