Recent content by summer

Thank you! I got it now.

Okay, so we know that if lambda is an eigenvector of A, then A(lambda) = (lambda)x, where x is the eigenvector. So in the case above Av3 = A(a1v1 + a2v2), it would be implied that a1v1 + a2v2 would also be an eigenvector belonging to lambda1. So, then, eigenvectors are unique to the...

Suppose for a given matrix A, Sarah finds the eigenvectors v1 = [1 3 4 5]' and v2 = [5 6 3 4]' form a base for eigenspace of labmda = 2. Now suppose Janie finds the eigenvectors v3 = [1 2 2 3]' and v4 = [7 8 7 6]' form a base for eigenspace of lambda = 4. Is Janie's solution compatible with...

A set S of (necessarily square) matrices is said to be closed under multiplication if AB∈ S whenever A, B ∈ S. Which of these matrices are closed under multiplication? Circulant matrices Upper triangular matrices Hessenberg matrices My trouble: How do I go about figuring this one out?