Linear Algebra Review and Reference
نویسنده
چکیده
3 Operations and Properties 7 3.1 The Identity Matrix and Diagonal Matrices . . . . . . . . . . . . . . . . . . 8 3.2 The Transpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 Symmetric Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 The Trace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.5 Norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.6 Linear Independence and Rank . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.7 The Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.8 Orthogonal Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.9 Range and Nullspace of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . 12 3.10 The Determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.11 Quadratic Forms and Positive Semidefinite Matrices . . . . . . . . . . . . . . 17 3.12 Eigenvalues and Eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.13 Eigenvalues and Eigenvectors of Symmetric Matrices . . . . . . . . . . . . . 19
منابع مشابه
Corrigendum to "On $(sigma, tau)$-module extension Banach algebras"
In this corrigendum, we give a correction of one result in reference [1].
متن کاملA 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 کاملCS189: Linear algebra review
This note is intended to provide the reader with the necessary linear algebra background to mathematically understand several fundamental topics in machine learning we will be discussing in this course, including (but not limited to) principle component analysis (PCA), singular value decomposition (SVD), and spectral clustering. I am assuming the reader is familiar with Math 54 level concepts f...
متن کاملSome 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.
متن کاملStudy of Spatial Data Quality Elements and VGI Linear Data Quality Assessment Methods
Volunteered Geographic Information has provided a rich and valuable resource for spatial data in a variety of applications. Despite the many benefits, this information does not provide any guarantee for their quality. So far, there are several methods to determine the quality of VGI. In addition to introducing quality elements and their evaluation methods, the present study attempts to explore ...
متن کامل