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In-place matrix transposition. In-place matrix transposition, also called in-situ matrix transposition, is the problem of transposing an N × M matrix in-place in computer memory, ideally with O (1) (bounded) additional storage, or at most with additional storage much less than NM. Typically, the matrix is assumed to be stored in row-major or ...
NumPy. NumPy (pronounced / ˈnʌmpaɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [ 3] The predecessor of NumPy, Numeric, was originally created by Jim Hugunin with ...
In computing, row-major order and column-major order are methods for storing multidimensional arrays in linear storage such as random access memory . The difference between the orders lies in which elements of an array are contiguous in memory. In row-major order, the consecutive elements of a row reside next to each other, whereas the same ...
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A T (among other notations). [1] The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. [2]
Moore–Penrose inverse. In mathematics, and in particular linear algebra, the Moore–Penrose inverse of a matrix , often called the pseudoinverse, is the most widely known generalization of the inverse matrix. [ 1] It was independently described by E. H. Moore in 1920, [ 2] Arne Bjerhammar in 1951, [ 3] and Roger Penrose in ...
Definition. The adjugate of A is the transpose of the cofactor matrix C of A , In more detail, suppose R is a unital commutative ring and A is an n × n matrix with entries from R. The (i, j) - minor of A, denoted Mij, is the determinant of the (n − 1) × (n − 1) matrix that results from deleting row i and column j of A.
Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.
Dot product. In mathematics, the dot product or scalar product[ note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors ), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or ...