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  2. Matrix (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Matrix_(mathematics)

    In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.

  3. Definite matrix - Wikipedia

    en.wikipedia.org/wiki/Definite_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 . [1] More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector , where denotes the ...

  4. Invertible matrix - Wikipedia

    en.wikipedia.org/wiki/Invertible_matrix

    In linear algebra, an invertible matrix is a square matrix which has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an inverse to undo the operation. An invertible matrix multiplied by its inverse yields the identity matrix. Invertible matrices are the same size as their ...

  5. List of named matrices - Wikipedia

    en.wikipedia.org/wiki/List_of_named_matrices

    A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries. Matrices have a long history of both study and application, leading to diverse ways of classifying matrices. A first group is matrices satisfying concrete conditions of the entries, including constant matrices.

  6. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    Matrix multiplication shares some properties with usual multiplication. However, matrix multiplication is not defined if the number of columns of the first factor differs from the number of rows of the second factor, and it is non-commutative, [10] even when the product remains defined after changing the order of the factors. [11] [12]

  7. Unitary matrix - Wikipedia

    en.wikipedia.org/wiki/Unitary_matrix

    In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U −1 equals its conjugate transpose U *, that is, if = =, where I is the identity matrix.. In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is denoted by a dagger (⁠ † ⁠), so the equation above is written

  8. Commuting matrices - Wikipedia

    en.wikipedia.org/wiki/Commuting_matrices

    The property of two matrices commuting is not transitive: A matrix may commute with both and , and still and do not commute with each other. As an example, the identity matrix commutes with all matrices, which between them do not all commute. If the set of matrices considered is restricted to Hermitian matrices without multiple eigenvalues ...

  9. Idempotent matrix - Wikipedia

    en.wikipedia.org/wiki/Idempotent_matrix

    Toggle Properties subsection. 3.1 Singularity and regularity. 3.2 Eigenvalues. ... In linear algebra, an idempotent matrix is a matrix which, when multiplied by ...