Matrix Calculator: Complex Matrix & Linear System Solver

Use our free online matrix calculator for matrix algebra with complex matrices (up to 10×10). Perform basic matrix operations—addition, subtraction, multiplication and division (by inversion). By applying elementary row operations, the calculator also carries out advanced matrix operations, including finding the determinant, inverse, and adjugate for n×n (square) matrices. Also, for an m×n matrix, you can find the rank or transform the matrix into lower/upper triangular forms or reduced row echelon form (RREF). Additionally, you can solve systems of linear equations via Gauss-Jordan elimination on augmented matrices with both real and imaginary entries. Furthermore, our advanced matrix solver lets you evaluate intricate matrix expressions involving up to eight complex matrices simultaneously—a capability exclusive to our matrix expression evaluator.

Quick Start

Set Up Your Matrix

  • Select: Choose a Matrix (A—H) from the dropdown menu.
  • Resize: Click the ＋ buttons or type dimensions directly into the input boxes.
  • Matrix entries: Enter numbers or constant expressions (e.g., 5/3 or (2+3i)sin(pi/2)).

Convenient Matrix Operations: Use the buttons at the top of the calculator (e.g., det for Matrix Determinant, inv for Inverse Matrix) to perform essential operations.

Quick Calculations: Use the dropdown list for common tasks like A*B or A+B.

Custom Expressions: Evaluate matrix expressions such as 2A + inv(BC) - D^3 by typing directly into the Expression Box.

Solve Linear Systems (e.g., Ax = b)

  1. Check the Linear System box. This turns the matrix interface into an Augmented Matrix by adding a highlighted column for the column vector (b).
  2. Fill in the coefficients A and the column vector b.
  3. Press Solve to view the solution and the RREF.

Note: The matrix calculator automatically saves dimensions, entries, and augmented settings for all matrices between visits. To wipe all data and start fresh, use the Reset Calculator button.

About the Matrix Calculator

One Interface for All Matrices: This innovative matrix calculator and linear system solver provides a single, dynamic interface to conveniently manage multiple matrices, including augmented matrices for linear systems of equations.

Our advanced matrix calculator is designed to efficiently perform matrix operations on up to 10×10 matrices. It offers full support for complex matrices—those containing real, imaginary, or complex entries.

Matrix Operations

Beyond elementary matrix operations, the calculator performs advanced operations on square matrices (e.g., finding the determinant or inverse). For matrices of any dimension, you can perform other advanced operations such as finding rank and RREF.

Matrix Expression Handling

What sets our calculator apart is its ability to evaluate intricate matrix expressions involving up to eight compatible matrices, such as: A+BCD-inv(E)

Solve Systems of Linear Equations

Our linear system solver uses Gaussian elimination to solve systems of linear equations by performing row operations on augmented matrices. As a complex augmented matrix calculator, it fully supports systems involving a complex coefficient matrix and a complex column vector representing the right-hand side of the system.

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Results

Elementary & Advanced Matrix Algebra

Suitable for all levels, this easy-to-use yet powerful complex matrix calculator simplifies and evaluates expressions involving complex matrices, performing operations ranging from basic arithmetic to advanced linear algebra.

Basic Matrix Operations

Perform fundamental matrix algebra with our online calculator:

Advanced Matrix Operations

Determinant, Inverse, and Adjugate

Calculate the following properties for square matrices:

Rank, Triangular Forms, RREF, and Transpose

Compute the following for matrices of any dimension: