Question

the dimension of the vector space of 7x7 real symmetric matrices with trace zero and the sum of the off-diagonal elements zero is

Answer 1

Answer:

Step-by-step explanation

You simply have to count all the numbers that you can put independantly in the matrix. You can put all the numbers you want in one half or the other (but it will fix the numbers in the other half since the matrix is symetric), and all the elements in the diagonal, except one, because the trace being 0 implies that the sum of the elements in the diagonal is 0 (it's the definition of the trace), so the last number is fixed, its value being the opposite of the sum of all the others elements in the diagonal.

That gives n2+n/2independant values, so the dimension you want is n2+n/2 =−1.