Basis of symmetric matrices

Algebra Level 3

What is the dimension of the basis of all real $N\times N$ symmetric matrices?

N^2

\dfrac{N^2+N}{2}

N

\dfrac{N^2-N}{2}

1 solution

Aareyan Manzoor
May 26, 2017

the basis consists first of the basis for all diagonal matrices, that is a matrix with a one one in one diagonal. there are $N$ of those. then the matrix has $N^2-N$ spots remaining. notice since two numbers are always the same, the dimension is $\dfrac{N^2-N}{2}$ . so the total dimension of the basis is $\dfrac{N^2-N}{2}+N=\dfrac{N^2+N}{2}$

Basis of symmetric matrices

1 solution

0 pending reports