Matrix Methods: An Introduction
This new edition of Matrix Methods emphasizes applications to Jordan-canonical forms, differential equations, and least squares. The revision now includes an entire new chapter on inner products, additional material on elementary row applications, and hundreds of new exercises.
* Provides an introduction to the functional approach to programming
* Emphasizes the problem to be solved, not the programming language
* Takes the view that all computer programs are a definition of a function
* Includes exercises for each chapter
* Requires at least a high school algebra level of mathematical sophistication
* A self-contained work
* Can be used as a pre-programming language introduction to the mathematics of computing
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algorithm arbitrary calculate canonical basis Cayley-Hamilton theorem characteristic equation cofactor column rank compute converges Cramer's rule defined in Problem denote described in Problem det(A Determine diagonal matrix differential equations dominant eigenvalue eigenvalue of multiplicity Eigenvector components Eigenvalue eigenvector of type elementary matrix elementary row operations equal Example 1 Find fundamental form Gaussian elimination given in Problem given matrices hence Hermitian matrix initial-value problem inner product inverse power method Iteration Eigenvector components Jordan canonical form left eigenvector linear combination linearly independent eigenvectors LU decomposition Markov chain matrix defined matrix form matrix given matrix in Problem n x n matrix Note obtain orthogonal orthonormal set pivot polynomial positive definite Problem 16 Proof QR-algorithm Redo Problem row-reduced form scalar second row Section 1.1 set of equations set of vectors Show Solution solve the system Specialize system 20 square matrix symmetric matrix third row transition matrix variables Verify Property zero