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Everything about Definite matrix
Property of a mathematical matrix
In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector where is the row vector transpose of More generally, a Hermitian matrix is positive-definite if the real number is positive for every nonzero complex column vector where denotes the conjugate transpose of Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Definite matrixA 5-minute orientation
- Skim a recent paper: Solving system of nonlinear matrix equations over Hermitian positive definite matricesInfluential work since 2022
- Pick up a classic book: Positive definite and definitizable functionsThe most-reprinted book on the subject
- Read the landmark paper: A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance MatrixCited 16,056 times
- Go sideways: Square root of a matrixA closely related topic
- Go sideways: Square matrixA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix
Semi-Definite Matrix Constraints in Optimization
Symmetric decomposition of a positive definite matrix
A Jacobi eigenreduction algorithm for definite matrix pairs
Nonnegative-definite and positive-definite solutions to the matrix equationAXA∗=B – revisited
Multisplitting of a Symmetric Positive Definite Matrix
On nonnegative definite solutions to matrix quadratic equations
Definite Matrix Polynomials and their Linearization by Definite Pencils
🆕 Influential since 2022
Solving system of nonlinear matrix equations over Hermitian positive definite matrices
Unique positive definite solution of non-linear matrix equation on relational metric spaces
Applying fixed point techniques for obtaining a positive definite solution to nonlinear matrix equations
Definite complete invariant parametrization of R -matrix theory
Manifold learning based on locally linear embedding for symmetric positive definite matrix
📚 Books worth reading
Positive definite and definitizable functionsZoltán Sasvári · 1994
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Square root of a matrix In mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if…
- Square matrix In mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n. Any two…
- Matrix decomposition In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices…
- Hermitian matrix In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose…
- Normal matrix In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*: A normal⟺A∗A=AA∗. The concept of normal matrices can…
- Gram matrix In linear algebra, the Gram matrix (or Gramian matrix, Gramian) of vectors v1,…,vn in an inner product space is the Hermitian matrix of inner products…
- Polar decomposition In mathematics, the polar decomposition of a square real or complex matrix A is a factorization of the form A=UP, where U is a unitary matrix, and P is…
- Definite quadratic form In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative)…