Linear and multilinear algebra; matrix theory Determinants Concept
Determinant
Summary
The determinant is the unique function of square matrices that is multilinear and alternating in the rows and is on the identity matrix. It is zero exactly for the singular matrices, over a field.
Where this leads
51 pages build on this one.
- Ball's existence theorem in nonlinear elasticity
- List of simple Lie groups
- Wigner D-matrix
- Jacobi's formula
- Regulator of a number field
- Solution of equations with degenerate kernels
- Compact symplectic group
- 6-j symbol
- Kiefer–Wolfowitz equivalence theorem
- Table of Lie groups
- Mairhuber–Curtis theorem
- Sylvester's determinant identity
- Fredholm determinant
- Multivariate analysis of variance
- Poincaré group
- Hadamard's inequality in Fredholm theory
- Representation theory of SU(2)
- 3-j symbol
- Matrix pencil
- Pfaffian
- Hadamard's inequality
- Special unitary group SU(n)
- Moments and orthogonal polynomials
- Wigner's classification
- SU(2)
- Dodgson condensation
- Bott's Morse-theoretic proof of periodicity
- Hadamard's maximal determinant problem
- Chebyshev system
- SL(2,C)
- Spin group
- Unimodular matrix
- Lindström–Gessel–Viennot lemma
- Kleinian group
- Optimal experimental design
- Exceptional Lie group E8
- Plücker coordinates
- Complex Monge–Ampère operator
- Discriminant of a number field
- Levy–Desplanques theorem
- Lorentz group
- Representation theory of the Lorentz group
- Kirchhoff's matrix tree theorem
- Coplanarity
- Pin group
- Alexander polynomial
- Fredholm minors
- Szegő limit theorems
- Exceptional Lie group G2
- Lattice (group)
- Bareiss algorithm
Further reading
- Web https://en.wikipedia.org/wiki/Determinant, As an alternating multilinear form
About this page
| Tag | 00KDZRW4C0 |
|---|---|
| URI | m2://00KDZRW4C0 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 15A15 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Ball's existence theorem in nonlinear elasticity
- Jacobi's formula
- Regulator of a number field
- Solution of equations with degenerate kernels
- Kiefer–Wolfowitz equivalence theorem
- Mairhuber–Curtis theorem
- Sylvester's determinant identity
- Fredholm determinant
- Multivariate analysis of variance
- Matrix pencil
- Pfaffian
- Hadamard's inequality
- Special unitary group SU(n)
- Moments and orthogonal polynomials
- Dodgson condensation
- Hadamard's maximal determinant problem
- Chebyshev system
- Unimodular matrix
- Lindström–Gessel–Viennot lemma
- Optimal experimental design
- Plücker coordinates
- Complex Monge–Ampère operator
- Discriminant of a number field
- Levy–Desplanques theorem
- Kirchhoff's matrix tree theorem
- Coplanarity
- Alexander polynomial
- Fredholm minors
- Szegő limit theorems
- Lattice (group)
- Bareiss algorithm