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Using Matrices

There are four functions that can be used when working with matrices.

Identity Matrix

An identity matrix is a square matrix which contains all zeros except the main diagonal contains ones

The inverse of a matrix is the matrix which when multiplied together gives the identity matrix.

MINVERSE

The MINVERSE() function returns the inverse of the matrix as an array formula.

This is usually entered as an array function and therefore must be entered with (Ctrl + Shift + Enter).

To find out more about Array Formulas and Functions, please refer to the Array Formulas section.

To prove that these are infact the correct inverses we need to multiply the two matrices together. This is shown below.

A matrix that has no inverse has a determinant of zero and is said to be singular.

MDETERM

The MDETERM() function returns the matrix determinant as an array formula.

This function only has an accuracy of 16 digits so a singular array may return a result that differs by 1E-16.

MMULT

The MMULT() function returns the product of two matrices.

This is usually entered as an array function and therefore must be entered with (Ctrl + Shift + Enter).

Matrix A multiplied by Matrix B is not the same as Matrix B multiplied by Matrix A (i.e. matrix multiplication is not commutative).

It is possible to use matrices to solve linear equations.

TRANSPOSE

The TRANSPOSE() function will transpose a matrix and return an array formula.

This is usually entered as an array function and therefore must be entered with (Ctrl + Shift + Enter).

The first row of the input array becomes the first column of the output array.

Things to Remember

When using the MDETERM, MINVERSE and MMULT functions every cell in the array must contain a numeric value. If not the function will return #VALUE!

A matrix with "m" rows and "n" columns is said to be of order (m * n). When "m" and "n" are equal then the matrix is said to be square.

Two matrices are said to be identical if every element in one matrix equals the corresponding element in the other matrix.

Matrix multiplication is not commutative so (A * B) does not equal (B * A).

Matrix division is undefined.

An identity matrix is a square matrix that contains all zeros except the main diagonal contains the value 1.