An 11 X 11 matrix B is called similar to A if there is a nonsingular n X 11 matrix T

Chapter 20, Problem 20.1.104

(choose chapter or problem)

\(\operatorname{det} \mathbf{A}=\lambda_{1} \lambda_{2} \cdots \lambda_{n}\)

Both formulas follow from the product representation of the characteristic polynomial, which we denote by \(f(\lambda)\),

\(f(\lambda)=(-1)^{n}\left(\lambda-\lambda_{1}\right)\left(\lambda-\lambda_{2}\right) \cdots\left(\lambda-\lambda_{n}\right) .\)

Text Transcription:

det A = lambda_1, lambda_2 . . . lambda_n

f(lambda)

f(lambda)=(-1)^n(lambda-lambda_1)(lambda-lambda_2)...(lambda-lambda_n).

lambda_1,...,lambda_r(r leqq n)