# Matrices

2017-07-31T11:35:42+03:00[Europe/Moscow] en true S-matrix, Rotation matrix, Givens rotation, Condition number, Identity matrix, Matrix similarity, Polynomial matrix, Water retention on mathematical surfaces, John Williamson (mathematician), Alternating sign matrix, Transformation matrix, Householder transformation, Diagonalizable matrix, Row and column spaces, Row and column vectors, Alternant matrix, Mooreâ€“Penrose pseudoinverse, Transpose, Adjugate matrix, Moore determinant of a Hermitian matrix, Kernel (linear algebra), Pauli matrices, Triangular matrix flashcards Matrices
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• S-matrix
In physics, the S-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process.
• Rotation matrix
In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
• Givens rotation
In numerical linear algebra, a Givens rotation is a rotation in the plane spanned by two coordinates axes.
• Condition number
In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument.
• Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
• Matrix similarity
In linear algebra, two n-by-n matrices A and B are called similar if for some invertible n-by-n matrix P.
• Polynomial matrix
In mathematics, a polynomial matrix or sometimes matrix polynomial is a matrix whose elements are univariate or multivariate polynomials.
• Water retention on mathematical surfaces
Water retention on mathematical surfaces refers to the water caught in ponds on a surface of cells of various heights on a regular array such as a square lattice, where water is rained down on every cell in the system.
• John Williamson (mathematician)
John Williamson (23 May 1901 – 1949) was a Scottish mathematician who worked in the fields of algebra, invariant theory, and linear algebra.
• Alternating sign matrix
In mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and −1s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign.
• Transformation matrix
In linear algebra, linear transformations can be represented by matrices.
• Householder transformation
In linear algebra, a Householder transformation (also known as Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin.
• Diagonalizable matrix
In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.
• Row and column spaces
In linear algebra, the column space C(A) of a matrix A (sometimes called the range of a matrix) is the span (set of all possible linear combinations) of its column vectors.
• Row and column vectors
In linear algebra, a column vector or column matrix is an m × 1 matrix, that is, a matrix consisting of a single column of m elements, Similarly, a row vector or row matrix is a 1 × m matrix, that is, a matrix consisting of a single row of m elements Throughout, boldface is used for the row and column vectors.
• Alternant matrix
In linear algebra, an alternant matrix is a matrix with a particular structure, in which successive columns have a particular function applied to their entries.
• Moore–Penrose pseudoinverse
In mathematics, and in particular linear algebra, a pseudoinverse A+ of a matrix A is a generalization of the inverse matrix.
• Transpose
In linear algebra, the transpose of a matrix A is another matrix AT (also written A′, Atr, tA or At) created by any one of the following equivalent actions: * reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain AT * write the rows of A as the columns of AT * write the columns of A as the rows of AT Formally, the i th row, j th column element of AT is the j th row, i th column element of A: If A is an m × n matrix then AT is an n × m matrix.