## Elementary Linear Algebra 7th Edition

The set W of all $n\times n$ diagonal matrices is a vector subspace of $M_{n,n}$.
The set W of all $n\times n$ diagonal matrices is a vector subspace of $M_{n,n}$. Because the sum of two diagonal matrices is a diagonal matrix and multiplying any diagonal matrix by a constant is a diagonal matrix which means that W is closed under addition and scalar multiplication.