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Complex Matrix Calculator & Linear System Solver

Our free online matrix calculator supports matrices up to 10×10 with real or complex entries. This advanced math calculator for matrix algebra allows you to evaluate expressions containing up to eight matrices simultaneously, or solve systems of linear equations via Gauss-Jordan elimination. As a linear algebra calculator, it is an ideal tool for basic matrix operations—addition, subtraction, multiplication, and division (via inverse matrix multiplication). It also handles advanced tasks like calculating the determinant, inverse, and rank, as well as converting to reduced row echelon form (RREF).

Quick Start
  • Select a matrix (A–H) from the drop-down list to fill or edit its entries (Matrix A is selected by default).
  • If desired, add rows or columns to the selected matrix by pressing the ＋ buttons.
  • You can also resize a selected matrix by entering the number of rows or columns in the text boxes provided, or by clicking the numbered buttons located to the left of a row or above a column.

Note: The matrix calculator retains the dimensions and entries of all matrices, as well as whether a matrix is augmented for solving systems of linear equations.

About the Matrix Calculator

Our advanced matrix calculator is designed to efficiently perform operations on matrices up to 10×10. 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, such as finding the determinant or the inverse. For matrices of any dimension, you can perform other advanced operations like finding the rank and RREF.

Matrix Expression Handling

What sets our matrix 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 Gauss-Jordan 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 intuitive yet powerful complex matrix calculator 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 these properties for square matrices:

Rank, Triangular Forms, RREF, and Transpose

Compute these properties for matrices of any dimension: