He not only explains how and why that is so, he also demonstrates linear algebra's nature through a wide variety of applications, covering vector spaces, Gaussian eliminations, eigenvalues and eigenvectors, determinants, calculating Jordan forms, normal linear spaces, inner product spaces
and orthogonality, matrices, singular values and related inequalities, pseudoinverses, difference equations and differential operations, vector related functions, external problems, matrix values holomorphic functions, realization theory, eigenvalue locator problems, zero location problems, convexity and matrices with nonnegative spaces.
Among specific topics are the structure of Hopf algebras, the growth of finitely generated solvable groups, uni-modular groups over number fields, isometries of inner product spaces
, and symmetric inner product spaces
over a Dedekind domain.
Calculation of Jordan forms is followed by normed linear spaces, inner product spaces
, orthogonality, and symmetric, Hermitian, and normal matrices.
Among the topics are inner product spaces
, discrete Fourier analysis, multi-resolution analysis, and the Daubechies wavelets.
The book begins with an introduction to vector spaces, inner product spaces
, and other preliminary topics in analysis.
The primary text covers linear equations, matrices, and determinants, Euclidean vector spaces, Rn, and general vector spaces, eigenvalues and eigenvectors, inner product spaces
, diagonalization and quadratic forms, general linear transformations, and numerical methods.
The authors (both professors of mathematics at the Rose- Hulman Institute of Technology) develop the mathematical framework of vector and inner product spaces
upon which signal and image processing depends; develop traditional Fourier-based transform techniques, primarily in the discrete case, but also somewhat in the continuous setting; and provide entry-level material on filtering, convolution, filter banks, and wavelets.
Among his topics are coordinates, the structure of a linear transformation, real and complex inner product spaces
, and matrix groups as Lie groups.
After transitioning from solving systems of two linear equations to solving general systems, this textbook introduces the algebraic properties of matrix operations, determinants, vector spaces, eigenvalues, eigenvectors, linear transformations, inner product spaces
, numerical techniques, and linear programming.
Their topics reflect the preferences in their own research over the past decade: discrete inequalities, integral inequalities for convex functions, Ostrowski and trapezoid type inequalities, Gruss type inequalities and related results, inequalities in inner product spaces
, and inequalities in normed linear spaces and for functionals.
offer more than 100 exercise while covering linear spaces, topological spaces, metric spaces, normed linear spaces and Banach spaces, inner product spaces
and Hilbert spaces, linear functionals, types of convergence in function space, reproducing kernel Hilbert spaces, order relations in function spaces, operators in function space, completely continuous operators, approximation methods for linear operator equations, interval methods for operator equations, contraction mappings and iterative methods, Newton's method in Banach spaces, variants of Newton's methods, and homotopy and continuation methods and a hybrid method for a free-boundary problem.