9. Change of basis/coordinates Theorem Let β and β be two ordered
... Let A, B ∈ Mn(F). The matrix B is said to be similar to A if there exists an invertible matrix P such that B = P −1AP. Theorem Assume the following: • V and W are finite dimensional vector spaces • T : V → W is linear • β and β 0 are ordered bases for V • γ and γ 0 are ordered bases for W Then we ha ...
... Let A, B ∈ Mn(F). The matrix B is said to be similar to A if there exists an invertible matrix P such that B = P −1AP. Theorem Assume the following: • V and W are finite dimensional vector spaces • T : V → W is linear • β and β 0 are ordered bases for V • γ and γ 0 are ordered bases for W Then we ha ...
October 28, 2014 EIGENVALUES AND EIGENVECTORS Contents 1.
... having degree n, and that the coefficient of λn is (−1)n . Definition 2. The polynomial det(M − λI) is called the characteristic polynomial of the matrix M , and the equation det(M − λI) = 0 is called the characteristic equation of M . Remark. Some authors refer to the characteristic polynomial as d ...
... having degree n, and that the coefficient of λn is (−1)n . Definition 2. The polynomial det(M − λI) is called the characteristic polynomial of the matrix M , and the equation det(M − λI) = 0 is called the characteristic equation of M . Remark. Some authors refer to the characteristic polynomial as d ...
