Search results
Results From The WOW.Com Content Network
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 first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB. [1]
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:
In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix.It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map with respect to a standard choice of basis.
Multiplication of two matrices is defined if and only if the number of columns of the left matrix is the same as the number of rows of the right matrix. If A is an m×n matrix and B is an n×p matrix, then their matrix product AB is the m×p matrix whose entries are given by dot product of the corresponding row of A and the corresponding column ...
A is a 10×30 matrix, B is a 30×5 matrix, C is a 5×60 matrix, and the final result is a 10×60 matrix. The regular polygon for this example is a 4-gon, i.e. a square: The matrix product AB is a 10x5 matrix and BC is a 30x60 matrix. The two possible triangulations in this example are:
The operation is a component-wise inner product of two matrices as though they are vectors, and satisfies the axioms for an inner product. The two matrices must have the same dimension—same number of rows and columns—but are not restricted to be square matrices .
The Cracovian product of two matrices, say A and B, is defined by A ∧ B = B T A, where B T and A are assumed compatible for the common type of matrix multiplication. Since ( AB ) T = B T A T , the products ( A ∧ B ) ∧ C and A ∧ ( B ∧ C ) will generally be different; thus, Cracovian multiplication is non- associative .
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).