Download PROBLEMS AND SOLUTIONS IN INTRODUCTORY AND ADVANCED MATRIX by Willi-Hans Steeb PDF

By Willi-Hans Steeb

This e-book offers an intensive selection of issues of particular suggestions in introductory and complex matrix calculus. Supplementary difficulties in every one bankruptcy will problem and excite the reader, excellent for either graduate and undergraduate arithmetic and theoretical physics scholars. The insurance contains structures of linear equations, linear differential equations, integration and matrices, Kronecker product and vec-operation in addition to capabilities of matrices. in addition, really good themes similar to spectral theorem, nonnormal matrices and at the same time impartial bases are incorporated. some of the difficulties are regarding purposes for crew idea, Lie algebra concept, wavelets, graph thought and matrix-valued differential types, benefitting physics and engineering scholars and researchers alike. It additionally branches out to issues of tensors and the hyperdeterminant. machine algebra courses in Maxima and SymbolicC++ have additionally been provided.

Contents:

  • Preface
  • Notation
  • Basic Operations
  • Linear Equations
  • Kronecker Product
  • Traces, Determinants and Hyperdeterminants
  • Eigenvalues and Eigenvectors
  • Spectral Theorem
  • Commutators and Anticommutators
  • Decomposition of Matrices
  • Functions of Matrices
  • Cayley–Hamilton Theorem
  • Hadamard Product
  • Norms and Scalar Products
  • vec Operator
  • Nonnormal Matrices
  • Binary Matrices
  • Star Product
  • Unitary Matrices
  • Groups, Lie teams and Matrices
  • Lie Algebras and Matrices
  • Braid Group
  • Graphs and Matrices
  • Hilbert areas and collectively impartial Bases
  • Linear Differential Equations
  • Differentiation and Matrices
  • Integration and Matrices
  • Bibliography
  • Index

Readership: Undergraduate and graduate scholars and researchers in arithmetic, physics and engineering.

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