Certain matrices are easier to work with than others. In this section, we will see how to write any square matrix M as the product of two simpler matrices.
Certain matrices are easier to work with than others. In this section, we will see how to write any square matrix M as the product of two simpler matrices.
What we will show next is that we can find a basis of Vsuch that the matrix M(T) is upper triangular. Since T is upper triangular with respect to the basis (v1,…,vn), we know th...What we will show next is that we can find a basis of Vsuch that the matrix M(T) is upper triangular. Since T is upper triangular with respect to the basis (v1,…,vn), we know that a1Tv1+⋯+ak−1Tvk−1∈\Span(v1,…,vk−1). Recall that λ∈F is an eigenvalue of T if and only if the operator T−λI is not invertible.
