matrix equation

However, the three cases may yield different matrix equations in general.

This is now a matrix equation, so it holds in any basis.

Since this is a matrix equation, it can be evaluated in any basis.

Any system of linear equations can be written as a matrix equation.

Direct computer algebra methods for matrix equations will also be introduced.

A more compact form of this matrix equation can be written as:

An iterative method is used to solve the matrix equation for the structure factor.

However, this matrix equation is solvable up to a multiplication and an addition.

They arise in solving matrix equations such as the Sylvester equation.

The Kronecker product can be used to get a convenient representation for some matrix equations.

As the method requires a very high accuracy, matrix equations need to be solved in double precision.

Given a matrix equation, use matrix inversion to find a solution.

Formally, this is a solution of the matrix equation by Jacobi iteration.

The matrix equation can be solved by well known methods such as Gauss elimination method.

A moment method is then used to reduce the integral equations to a matrix equation to compute the current coefficients.

This integral equation is then reduced to a matrix equation using the method of moments.

It also describes properties of the coefficient matrix in the matrix equation.

An efficient parallel algorithm for the solution of large sparse linear matrix equations.

Note that this property must be one of the variables held in the matrix equation future time-row state vector.

The matrix equation is equivalent to a homogeneous system of linear equations:

In other words, we want to solve this matrix equation for the vector on the right-hand side:

Standard method like Gauss elimination can be used to solve the matrix equation for .

This matrix equation is really two coupled equations:

Then we would need known distinct pairs to solve the equation by setting it up as a matrix equation.

These matrix equations can often be solved directly and efficiently when written as a matrix splitting.