Matrix Theory From Generalized Inverses to Jordan Form Chapman & Hall/CRC Pure and Applied Mathematics Series
Auteurs : Piziak Robert, Odell P.L.
In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class.
Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra.
With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.
Date de parution : 09-2019
15.2x22.9 cm
Date de parution : 02-2007
15.2x22.9 cm
Thèmes de Matrix Theory :
Mots-clés :
Full Rank Factorization; Ci Xi; Robert Piziak; Exercise Set; matrix theory; American Mathematical Monthly; MATLAB; Independent Set; fundamental subsapces; Minimal Polynomial; polynomials over C; Characteristic Polynomial; submatrices; Elementary Row Operations; determinants; Ref; Drazin Inverse; Geometric Multiplicity; Generalized Inverse; Full Row Rank; Block Diagonal; Permutation Matrix; Invertible Matrices; RREF; Affine Subspaces; LU Factorization; Smith Normal Form; Elementary Divisors; Bilinear Form; Direct Sum Decomposition; Jordan Blocks; Generalized Eigenvector