The set of all n × n matrices forms a vector space under addition and scalar multiplication, and familiar subspace concepts like basis, dimension, and intersection apply naturally.
Loading…
Vector space axioms satisfied by matrices
Record that any set closed under addition and scalar multiplication with the axioms holding is a vector space, and check the matrices with the zero matrix as identity.
Diagonal matrices as an intersection of subspaces
List the upper triangular, symmetric and diagonal subspaces, record the diagonal matrices as the intersection of the first two, and write out the basis of three matrices giving dimension .