Calculating Matrices

Complex Matrix Calculator

The Matrix Calculator allows you to do matrix algebra (matrix addition, matrix multiplication, matrix inverses, etc.) and solve systems of linear equations.

Matrix Algebra

Press the relevant buttons at the top of the Matrix Calculator to calculate the determinant, inverse, reduced row echelon form, adjugate, lower/upper triangular forms and transpose of the matrix A (initially selected).

You can do similarly as above with other matrices by first selecting them from the right side of the Matrix Calculator. Matrix entries can be complex numbers.

The matrices (A, B, C, ..., H ) are initially filled with 0's.

You can set the numbers of rows and columns of a matrix by pressing the buttons on the left or above the selected matrix, respectively. You can also add rows or add columnsby pressing the relevant + button.

This Matrix Calculator allows you to use any numeric (constant) expression, e.g., 1/2+3i2sin(3pi/2) for a matrix element.

Under the Quick Calculations you can calculate frequently used matrix expressions involving two or more matrices.

If a matrix expression is not listed under the quick calculation menu, you can enter it in the expression box provided and press Calculate.

The matrix expression can be in the most general form, such as (2+sin(π/3))A + inv(A+B/det(A))(B/2 + BC^4)/D^(3+2^5)

If the matrix expression is a valid expression and contains no operations of incompatible matrices, the result will be displayed. Otherwise an error message is displayed.

All 1x1 matrices are treated as scalars by this Matrix Calculator. They can be multiplied by any matrix (on either side) regardless of its dimension. Also if, for example A = [1/2], then sin(A) is treated as sin(1/2). Conversely, whenever appropriate, scalars are treated as 1x1 matrices. For example, inv(2) is treated as inv([2]) which will be given as 0.5.

This Matrix Calculator is also a Scientific Calculator. You can use it to calculate numeric expressions such as 2 + 3i + sin(π/3). To get the result of a calculation involving complex numbers in polar forms use Complex Number Calculator Polar.

You can also use this Matrix Calculator as a multi-variable function evaluator. Type in a function expression containing up to 8 variables (use A, B, C, ... as variables, instead of x,y,z, ...). Set all matrices involved as 1x1 matrices. Assign numbers (or constant expressions) to the variables (i.e., 1x1 matrices) and press Calculate. The value of the function is given as a scalar.

You can use the following in your expressions:

inv()

adj()

transp()

rref()

ut()

lt()

det()

1/A is the same as inv(A)

A/B is the same as Ainv(B)

Solving Linear Systems

Enter the augmented matrix and press RREF (Reduced Row Echelon Form). If the coefficient matrix is a square matrix and the system has a unique solution, the right-hand-side column will be the solution to the given linear system of equations.

Complex Linear System Solver

The following, which is a more proper way of solving linear systems, will be available in the future.

To solve a system of linear equations with coefficient matrix, say A, first select the Linear System check-box. Then enter the associated column vector (the right hand side of the equation) in the highlighted column adjacent to A to form the associated augmented matrix and press Solve.

The reduced row echelon form of the augmented matrix will be displayed on a separate window. If the coefficient Matrix is a square matrix and the system has a unique solution, the vector representing the unique solution will also be displayed.