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Details for:
Herstein I., Winter D. A Primer on Linear Algebra 1988
herstein i winter d primer linear algebra 1988
Type:
E-books
Files:
1
Size:
42.8 MB
Uploaded On:
May 25, 2022, 9:01 a.m.
Added By:
andryold1
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0
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Info Hash:
BCC0005B947C2F91B61F2E24F959166E84BECA88
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Textbook in PDF format Preface Contents Symbol List The 2x2 matrices Introduction Definitions and operations Some notation Trace, transpose, and odds and ends Determinants Cramer's rule Mappings Matrices as mappings The Cayley-Hamilton theorem Complex numbers M(C) Inner products Systems of linear equations Introduction Equivalent systems Elementary row operations, echelon matrices Solving systems of linear equations The nxn matrices The opening Matrices as operators Trace Transpose and Hermitian adjoint Inner product spaces Bases of F^(n) Change of basis of F^(n) Invertible matrices Matrices and bases Bases and inner products More on nxn matrices Subspaces More on subspaces Gram-Schmidt orthogonalization process Rank and nullity Characteristic roots Hermitian matrices Triangularizing matrices with complex entries Exponentials Determinants Introduction Properties of determinants: row operations Properties of determinants: column operations Cramer's rule Properties of determinants: other expansions Elementary matrices The determinant of the product The characteristic polynomial The Cayley-Hamilton theorem Rectangular matrices More on systems of linear equations Rectangular matrices Linear transformations from F^(n) to F^(m) The nullspace and column space of an mxn matrix Abstract vector spaces Introduction, definitions, and examples Subspaces Homomorphisms and isomorphisms Isomorphisms from V to F^(n) Linear independence in infinite-dimensional vector spaces Inner product spaces More on inner product spaces Linear transformations Introduction Definitions, examples, and some preliminary results Products of linear transformations Linear transformations as matrices Hermitian ideas Linear transformations from one space to another Applications Fibonacci numbers Equations of curves Markov processes Incidence models Differential equations Least squares methods Approximate solutions of systems of linear equations The approximate inverse of an mxn matrix Solving a matrix equation using its normal equation Finding functions that approximate data Linear algorithms Introduction The LDU factorization of A The row reduction algorithm and its inverse Back and forward substitution Solving Ax = y Approximate inverse and projection algorithms A computer program for finding exact and approximate solutions Index
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Herstein I., Winter D. A Primer on Linear Algebra 1988.pdf
42.8 MB