Basic matrix algebra

Basic Algebra

This chapter is mostly a review, discussing unique factorization of positive integers, unique factorization of polynomials whose coefficients are rational or real or complex, signs of permutations, and matrix algebra. Sections 1–2 concern unique factorization of positive integers. Section 1 proves the division and Euclidean algorithms, used to compute greatest common divisors. Section 2 establi...

Local Basic Linear Algebra

We describe a subset of the level{1, level{2, and level{3 BLAS implemented for each node of the Connection Machine system CM{200. The routines, collectively called LBLAS, have interfaces consistent with languages with an array syntax such as Fortran 90. One novel feature, important for distributed memory architectures, is the capability of performing computations on multiple instances of object...

Basic Abstract Algebra Factbook

2 Groups 3 2.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Homomoprphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Direct and Semidirect Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Normal Subgroups . . . . . . . . . . . . . . . . . . . . . ....

Notes on Basic Homological Algebra

Some results on Haar wavelets matrix through linear algebra

Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.