Linear and multilinear algebra; matrix theory Special matrices Concept
Positive semidefinite matrix
Summary
A positive semidefinite matrix is a Hermitian matrix with for every vector .
Where this leads
27 pages build on this one.
- Schoenberg's embedding criterion
- Legendre condition
- Loewner order
- Hadamard's inequality in Fredholm theory
- Discrete-time algebraic Riccati equation
- Algebraic Riccati equation
- Hadamard's inequality
- Positivity of Hankel matrices of moments
- Linear-quadratic-Gaussian control
- Choi's theorem on completely positive maps
- Riccati differential equation of optimal control
- Hadamard's maximal determinant problem
- Linear-quadratic regulator
- Gauss–Markov theorem
- Operator monotone function
- Krein's condition
- Multidimensional scaling
- Carleman's condition
- Verification theorem
- Hamburger moment problem
- Schur product theorem
- Separation principle
- Generalized least squares
- Stieltjes moment problem
- Trigonometric moment problem
- Nevanlinna parametrization of solutions
- Bareiss algorithm
Further reading
- Web https://en.wikipedia.org/wiki/Definite_matrix, Definitions
About this page
| Tag | 01MMVW8CKC |
|---|---|
| URI | m2://01MMVW8CKC |
| Kind | concept |
| Writing | W1 stated |
| MSC | 15B57, 15A63 |
| Specializes | Hermitian matrix |
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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)
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What links here
Definitions
Special cases
Used by
- Schoenberg's embedding criterion
- Legendre condition
- Loewner order
- Discrete-time algebraic Riccati equation
- Algebraic Riccati equation
- Hadamard's inequality
- Positivity of Hankel matrices of moments
- Linear-quadratic-Gaussian control
- Choi's theorem on completely positive maps
- Riccati differential equation of optimal control
- Linear-quadratic regulator
- Gauss–Markov theorem
- Operator monotone function
- Multidimensional scaling
- Hamburger moment problem
- Schur product theorem
- Stieltjes moment problem
- Trigonometric moment problem