The prototypical multilinear operation is multiplication. Indeed, every multilinear mapping can be factored through a tensor product. Apart from its intrinsic interest, the tensor product is of fundamental importance in a variety of disciplines, ranging from matrix inequalities and group representation theory, to the combinatorics of symmetric functions, and all these subjects appear in this book. Another attraction of multilinear algebra lies in its power to unify such seemingly diverse topics. This is done in the final chapter by means of the rational representations of the full linear group. Arising as characters of these representations, the classical Schur polynomials are one of the keys to unification. Prerequisites for the book are minimized by self-contained introductions in the early chapters. Throughout the text, some of the easier proofs are left to the exercises, and some of the more difficult ones to the references.
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First Sentence:
The integer 6 is said to be "perfect" because it is the sum of its proper divisors: 6 = 1 + 2 + 3. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
decomposable symmetrized tensors, disjoint cycle factorization, permanental roots, generalized matrix functions, immanantal polynomials, homogeneous polynomial invariants, permanental dominance conjecture, multiplicity partition, cycle index polynomial, monomial symmetric functions, nonisomorphic graphs, decomposable tensors, independent indeterminates, irreducible character, character afforded, alternating character, positive semidefinite hermitian, same cycle structure, multilinear algebra, irreducible constituent, distinct representatives, pattern inventory, induced basis, stabilizer subgroup, inequivalent irreducible representations Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Universal Factorization Property, Dias da Silva, Schur's Inequality, Proof Suppose, Burnside's Lemma, Orthogonality Relations of the Second Kind, Gamas's Theorem, Orthogonality Relations of the First Kind, Schur Relations, Weyl's Principle, Hadamard's Theorem, Application Exercises, Burnside's Theorem, Maschke's Theorem, Watkins's Theorem, Fischer's Inequality, Graphs Let, Hadamard's Inequality, Mimic Example, Use Equation, Use Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The integer 6 is said to be "perfect" because it is the sum of its proper divisors: 6 = 1 + 2 + 3. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
decomposable symmetrized tensors, disjoint cycle factorization, permanental roots, generalized matrix functions, immanantal polynomials, homogeneous polynomial invariants, permanental dominance conjecture, multiplicity partition, cycle index polynomial, monomial symmetric functions, nonisomorphic graphs, decomposable tensors, independent indeterminates, irreducible character, character afforded, alternating character, positive semidefinite hermitian, same cycle structure, multilinear algebra, irreducible constituent, distinct representatives, pattern inventory, induced basis, stabilizer subgroup, inequivalent irreducible representations Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Universal Factorization Property, Dias da Silva, Schur's Inequality, Proof Suppose, Burnside's Lemma, Orthogonality Relations of the Second Kind, Gamas's Theorem, Orthogonality Relations of the First Kind, Schur Relations, Weyl's Principle, Hadamard's Theorem, Application Exercises, Burnside's Theorem, Maschke's Theorem, Watkins's Theorem, Fischer's Inequality, Graphs Let, Hadamard's Inequality, Mimic Example, Use Equation, Use Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 30
books:
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14
books
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- Multilinear Algebra (Universitext) by Werner Greub in Front Matter, and Back Matter
- Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications) by Richard A. Brualdi in Back Matter
- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Back Matter
- Matrix Analysis by Roger A. Horn in Back Matter
- A Survey of Matrix Theory and Matrix Inequalities (Dover Books on Mathematics) by Marvin Marcus in Back Matter
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- Permanents (Encyclopedia of Mathematics and its Applications) by Henryk Minc in Back Matter (1), Back Matter (2), and Back Matter (3)
- Eigenspaces of Graphs (Encyclopedia of Mathematics and its Applications) by Dragos Cvetkovic in Back Matter (1), and Back Matter (2)
- Matrix Theory by Fuzhen Zhang in Back Matter (1), and Back Matter (2)
- Hyperidentities and Clones (Algebra, Logic and Applications Series Volume 14) by Klaus Denecke in Front Matter
- Ordered Algebraic Structures (Algebra, Logic and Applications) by W. Charles Holland in Front Matter
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