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008			220601s2021 sz | s |||| 0|eng d
020			_a9783031025440
024	7		_a10.1007/978-3-031-02544-0 _2doi
040			_aES-MaUEC _bspa _cES-MaUEC _dES-MaUEC
050		4	_aTA347.L5 _b2021 EB
100	1		_aKanatani, Kenʼichi, _eautor _4aut _4http://id.loc.gov/vocabulary/relators/aut _9101824 _d1947-
245	1	0	_aLinear Algebra for Pattern Processing : _bProjection, Singular Value Decomposition, and Pseudoinverse _cby Kenichi Kanatani
250			_a1st edition 2021
264		1	_aCham _bSpringer International Publishing _c2021
300			_a1 recurso en línea (XIV, 141 páginas)
336			_atexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
347			_aarchivo de texto _bPDF
490	0		_aSynthesis Lectures on Signal Processing _x1932-1694
505	0		_aPreface -- Introduction -- Linear Space and Projection -- Eigenvalues and Spectral Decomposition -- Singular Values and Singular Value Decomposition -- Pseudoinverse -- Least-Squares Solution of Linear Equations -- Probability Distribution of Vectors -- Fitting Spaces -- Matrix Factorization -- Triangulation from Three Views -- Bibliography -- Author's Biography -- Index.
520			_aLinear algebra is one of the most basic foundations of a wide range of scientific domains, and most textbooks of linear algebra are written by mathematicians. However, this book is specifically intended to students and researchers of pattern information processing, analyzing signals such as images and exploring computer vision and computer graphics applications. The author himself is a researcher of this domain. Such pattern information processing deals with a large amount of data, which are represented by high-dimensional vectors and matrices. There, the role of linear algebra is not merely numerical computation of large-scale vectors and matrices. In fact, data processing is usually accompanied with "geometric interpretation." For example, we can think of one data set being "orthogonal" to another and define a "distance" between them or invoke geometric relationships such as "projecting" some data onto some space. Such geometric concepts not only help us mentally visualize abstract high-dimensional spaces in intuitive terms but also lead us to find what kind of processing is appropriate for what kind of goals. First, we take up the concept of "projection" of linear spaces and describe "spectral decomposition," "singular value decomposition," and "pseudoinverse" in terms of projection. As their applications, we discuss least-squares solutions of simultaneous linear equations and covariance matrices of probability distributions of vector random variables that are not necessarily positive definite. We also discuss fitting subspaces to point data and factorizing matrices in high dimensions in relation to motion image analysis. Finally, we introduce a computer vision application of reconstructing the 3D location of a point from three camera views to illustrate the role of linear algebra in dealing with data with noise. This book is expected to help students and researchers of pattern information processing deepen the geometric understanding of linear algebra.
988			_aSynthesis Collection of Technology_2021
650		7	_2embne _9152614 _aReconocimiento de formas _xModelos matemáticos
650		7	_2embne _9140933 _aÁlgebra lineal
776	0	8	_iPrinted edition: _z9783031003370
776	0	8	_iPrinted edition: _z9783031014161
776	0	8	_iPrinted edition: _z9783031036729
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-031-02544-0 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942			_2lcc _cLE
998			_b01/2023 _dz _esc _zSI