matrix addition

It is defined using the Kronecker product and normal matrix addition.

The usual matrix addition is defined for two matrices of the same dimensions.

Applying further simplification and basic rules of matrix addition we come up with the following:

Matrix multiplication is distributive over matrix addition, though also not commutative.

The operations of matrix addition and matrix multiplication are especially simple for diagonal matrices.

The z-parameters of the combined network are found by matrix addition of the two individual z-parameter matrices.

In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together.

The set of all 2 x 2 matrices is also a ring, under matrix addition and matrix multiplication.

Addition and multiplication of split-complex numbers are then given by matrix addition and multiplication.

The set of all n by n matrices over a given ring, with matrix addition or matrix multiplication as the operation.

Each ballot can be transformed into this style of matrix, and then added to all other ballot matrices using matrix addition.

One can check that with the operations of matrix addition and matrix multiplication, this set satisfies the above ring axioms.

Then the set of all square matrices of size n forms a ring with the usual matrix addition and matrix multiplication.

Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.

In abstract algebra, a matrix ring is any collection of matrices forming a ring under matrix addition and matrix multiplication.

The conjugate transpose can be motivated by noting that complex numbers can be usefully represented by 2x2 real matrices, obeying matrix addition and multiplication:

There are at least two ways of representing quaternions as matrices in such a way that quaternion addition and multiplication correspond to matrix addition and matrix multiplication.

There are a number of basic operations that can be applied to modify matrices, called matrix addition, scalar multiplication, transposition, matrix multiplication, row operations, and submatrix.

Since the two processors work in parallel, the job of performing matrix addition would take one half the time of performing the same operation in serial using one CPU alone.

Matrix addition and multiplication make the set of all n x n matrices into an associative algebra and hence there is a corresponding representation theory of associative algebras.

In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and the algebraic operations in terms of matrix addition and matrix multiplication.

The sum and product of dual numbers are then calculated with ordinary matrix addition and matrix multiplication; both operations are commutative and associative within the algebra of dual numbers.

Addition and multiplication are carried out using the usual rules of matrix addition and matrix multiplication; the heights and widths of the matrices have been chosen so that multiplication is defined.

This is done by the creation of a grid, whose cavities have wells of varying depth, according to the matrix addition of two quadratic sequences equal or proportionate to those of a regular diffusor.

Support for handling arrays of data was relatively strong, with statements able to read an entire array from statements, and perform useful matrix operations such as matrix addition, matrix subtraction, matrix multiplication, and finding the inverse matrix for a square matrix.