As we've journeyed together through the realms of linear algebra, we've uncovered the powers of matrices in transforming shapes and spaces, akin to casting spells that reshape our perception of the ...

Eigenvalues and eigenvectors are foundational concepts in linear algebra, with extensive applications across various domains such as physics, computer graphics, and machine learning. These concepts ...

Abstract: In this paper, the eigenvalues and eigenvectors of the generalized discrete Fourier transform (GDFT), the generalized discrete Hartley transform (GDHT), the type-IV discrete cosine transform ...

Abstract: An analytic parahermitian matrix admits in almost all cases an eigenvalue decomposition (EVD) with analytic eigenvalues and eigenvectors. We have previously defined a discrete Fourier ...

These two multiplications display a unique behavior to other matrix products. Matrices can be considered linear transformation operations performed on a vector. When multiplied by the matrix, these ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

Here are three examples that we will consider. In each case, we have pre-computed the eigenvalues and eigenvectors (check them yourself). \[ A = \begin{bmatrix} 2 & 2 ...

This is a preview. Log in through your library . Publisher Information "The Society for Industrial and Applied Mathematics is a leading international association for applied mathematics, and its ...