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 ...

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 ...

Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained ...

Abstract: The discrete quaternion Fourier transform (DQFT) is useful for signal analysis and image processing. In this paper, we derive the eigenfunctions and eigenvalues of the DQFT. We also extend ...

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 ...

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 ...

Abstract: In addition to the basic crystalline and amorphous structures for solids, it is possible that solids may also form with a quasiperiodic, or Penrose tile, structure. A current problem in ...