Matrix A, defined as A=[a,1;0,a], and matrix B, defined as B=[a,0;0,a], are not similar if B cannot be expressed as B ≠ Inv(P)*A*P for any invertible matrix P. While demonstrating this inequality is sufficient, a more straightforward method involves comparing the eigenvalues and corresponding eigenvectors of both matrices. The eigenvalue approach provides a clearer understanding of their similarity status.
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cutesteph said:Homework Statement
A=[a,1;0,a] B=[a,0;0,a]
If I want to show if matrix A is NOT similar to matrix B. Is it enough to show that B=/=Inv(P)*A*P? Or would I need to show that they do not have both the same eigenvalues and corresponding eigenvectors?