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In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the ...
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop: Input: matrices A and B.
Multiplication algorithm. A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the topic. The oldest and simplest method, known since antiquity as long ...
Permutation matrix. In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column with all other entries 0. [ 1]: 26 An n × n permutation matrix can represent a permutation of n elements. Pre- multiplying an n -row matrix M by a permutation matrix P ...
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.
In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [ 1] —hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: The general form is. Note that a is both a "first" term and an "outer" term; b is both a "last" and "inner" term, and so forth.
The DFT is (or can be, through appropriate selection of scaling) a unitary transform, i.e., one that preserves energy. The appropriate choice of scaling to achieve unitarity is , so that the energy in the physical domain will be the same as the energy in the Fourier domain, i.e., to satisfy Parseval's theorem. (Other, non-unitary, scalings, are ...
C [ i ][ j] = C [ i ][ j] + A [ i ][ k ]* B [ k ][ j ] output C (as A*B) This algorithm requires, in the worst case, multiplications of scalars and additions for computing the product of two square n×n matrices. Its computational complexity is therefore , in a model of computation where field operations (addition and ...