1. ### Find the eigenvalues and eigenvectors

Homework Statement Find the eigenvalues and eigenvectors fro the matrix: $$A=\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}$$. Homework Equations Characteristic polynomial: ## \nabla \left( t \right) = t^2 - tr\left( A \right)t + \left| A \right|## . The Attempt at a Solution I've found...
2. ### How are Faces Encoded for Image Recognition?

Hi all, I think I have an idea of how the Mathematical aspects of Face recognition work. But I am curious as to what an eigenvector would be in this respect. I am trying to understand it through finding out how pixels are encoded: What map takes a pixel into a collection of...

11. ### Norm indueced by a matrix with eigenvalues bigger than 1

Suppose we pick a matrix M\in M_n(ℝ) s.t. all its eigenvalues are strictly bigger than 1. In the question here the user said it induces some norm (|||⋅|||) which "expands" vector in sense that exists constant c∈ℝ s.t. ∀x∈ℝ^n |||Ax||| ≥ |||x||| . I still cannot understand why it's correct. How...
12. ### Eigenvalues and Eigenvectors

What does it mean when it says eigenvalues of Matrix (3x3) A are the square roots of the eigenvalues of Matrix (3x3) B and the eigenvectors are the same for A and B?
13. ### Finding eigenvalues with QR method

Hi, I am trying to solve the problem of finding eigenvalus for a general square symmetric matrix with the QR algorithm. I have understood that this task is much easier if the matrix is in an Hessemberg form, so I have implemented a function that does that with the Housholder method, but I can't...
14. ### Physical significance of Eigenvalues and Eigenvector?

I want to know what exactly Eigen value imply. What is its Physical significance ? Physical significance of eigen vector? Does eigen value concept apply in signal processing or evalvating frequency response off a system?