Suppose $V$ is a vector space. Given some vectors in $V$, we can add them with every nice property we might expect: associativity, an identity, inverses, and ...

Seems like GE on a 2x2 matrix should be pretty darn fast.... especially if you use scalar * vector type operations.

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 ...

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 ...

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 ...

Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons ...

Abstract Let A be an n × n Hermitian matrix and A = UΛUH be its spectral decomposition, where U is a unitary matrix of order n and Λ is a diagonal matrix. In this note we present the perturbation ...