Linear algebra – a brief review
نویسنده
چکیده
Matrices of dimensions m × 1 and 1 × n are called column and row vectors, respectively. We will typically denote column and row vectors by lower case Latin letters, e.g. a, b, x, y and other matrices by upper case Latin letters, e.g. A, B, X, Y . The scalars (or 1 × 1 matrices) will be frequently denoted by Greek letters α, β, λ, μ, etc. Unless stated otherwise, all scalars will be real numbers. Operations with matrices 1. (multiplication by a scalar) For any m× n matrix A = (aij)m×n and ∀α ∈ R, αA := (αaij)m×n. 2. (matrix multiplication) If A = (aij)m×p and B = (bij)p×n, then
منابع مشابه
A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices
The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...
متن کاملReview of Linear System Theory
The following is a (very) brief review of linear system theory and Fourier analysis. I work primarily with discrete signals, but each result developed in this review has a parallel in terms of continuous signals and systems. I assume the reader is familiar with linear algebra (as reviewed in my handout Geometric Review of Linear Algebra), and least squares estimation (as reviewed in my handout ...
متن کاملA case report and brief review of the literature of an unusual vascular malformation: linear verrucous hemangioma
Verrucous hemangiomas (VH) are uncommon, congenital vascular malformations of the cutaneous and subcutaneous tissues that spare the deeper subfacial structures. VH usually presents at birth and slowly grows with age. It usually presents as hyperkeratotic, scattered, bluish-red plaques or nodules of various sizes. Although the lesions mostly have a linear pattern, serpiginous and reticulat...
متن کاملReview: Statistics, Estimation and Decisions
The following is a (very) brief review of statistics, described from a Bayesian perspective, in the context of both experimental data analysis and modeling. I emphasize brevity and geometric intuition, at the expense of rigor and detail. I assume the reader is familiar with linear algebra (as reviewed in my handout Geometric Review of Linear Algebra), and least squares estimation (as reviewed i...
متن کاملReview of Linear Algebra Definitions, Change of Basis, Trace, Spectral Theorem
Matrices can be thought of as rectangular (often square) arrays of numbers, or as linear transformations from one space to another (or possibly to the same space). The former picture is the simplest starting point, but it is the latter, geometric view that gives a deeper understanding. We content ourselves in these notes with giving a brief review of some of the definitions and results of Linea...
متن کاملLinearization method in classification problems of linear algebra
The author devised in [Math. USSR–Izv. 31 (1988) 481– 501] a procedure that reduces the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings. We give a brief exposition of this method, review results that were obtained by using this method (and were published mainly in Russian), and give examples of classification problems that can...
متن کامل