Matrix Addition Calculator
Add two matrices of compatible dimensions, element by element.
Open calculator
AVAILABLE CALCULATORS
Matrix calculators
Start with one of the matrix operations below. Each calculator has its own page, so you can go directly to the calculation you need. Eigenvalue and eigenvector tools are limited to the matrix sizes and methods supported by their respective pages.
Matrix Subtraction Calculator
Subtract one matrix from another when their dimensions match.
Open calculatorMatrix Multiplication Calculator
Multiply compatible matrices and calculate the resulting matrix.
Open calculatorMatrix Scalar Multiplication Calculator
Multiply every entry of a matrix by a scalar value.
Open calculatorMatrix Calculator
Perform common matrix operations with a convenient matrix calculator.
Open calculatorMatrix Transpose Calculator
Exchange matrix rows and columns to calculate the transpose.
Open calculatorMatrix Determinant Calculator
Calculate the determinant of a square matrix.
Open calculatorMatrix Inverse Calculator
Find the inverse of an invertible square matrix.
Open calculatorMatrix Trace Calculator
Calculate the trace by summing the main diagonal entries of a square matrix.
Open calculatorMatrix Rank Calculator
Determine matrix rank using independent rows, columns, and elimination.
Open calculatorPositive Definite Matrix Test
Test whether a matrix satisfies positive definiteness criteria.
Open calculatorMatrix Norm Calculator
Calculate Frobenius, one, infinity, and maximum-entry matrix norms.
Open calculatorFrobenius Norm Calculator
Calculate the square root of the sum of squared matrix entries.
Open calculatorCondition Number Calculator
Assess matrix conditioning and numerical sensitivity.
Open calculatorMatrix Power Calculator
Calculate nonnegative integer powers of a square matrix.
Open calculatorKronecker Product Calculator
Calculate the Kronecker product of two matrices.
Open calculatorEigenvalue Calculator
Calculate eigenvalues for supported square matrix inputs.
Open calculatorEigenvector Calculator
Calculate eigenvectors associated with matrix eigenvalues.
Open calculatorCharacteristic Polynomial Calculator
Calculate the characteristic polynomial det(λI − A) of a square matrix.
Open calculatorMatrix Diagonalization Calculator
Determine whether a matrix is diagonalizable and find a suitable decomposition.
Open calculatorLU Decomposition Calculator
Factor a matrix into lower and upper triangular matrices when supported.
Open calculatorSingular Value Decomposition Calculator
Compute singular values and singular vectors for supported matrices.
Open calculatorSystem of Equations Calculator
Solve systems of linear equations and identify their solution types.
Open calculatorGaussian Elimination Calculator
Solve linear systems using Gaussian elimination and row operations.
Open calculatorReduced Row Echelon Form Calculator
Transform a matrix into reduced row echelon form using elementary row operations.
Open calculatorCramer's Rule Calculator
Solve suitable square linear systems using determinants and Cramer’s rule.
Open calculatorVector Calculator
Perform common vector operations and calculations in supported dimensions.
Open calculatorDot Product Calculator
Calculate the dot product of vectors and explore their angle relationship.
Open calculatorCross Product Calculator
Calculate the cross product of three-dimensional vectors.
Open calculatorRotation Matrix Calculator
Construct rotation matrices for supported two-dimensional or three-dimensional rotations.
Open calculatorCovariance Matrix Calculator
Calculate covariance matrices from multivariable observations.
Open calculatorJacobian Matrix Calculator
Calculate Jacobian matrices for multivariable functions with supported expressions.
Open calculatorMarkov Matrix Calculator
Analyze transition matrices and calculate state probabilities.
Open calculatorPageRank Matrix Calculator
Estimate page importance using transition probabilities and damping.
Open calculatorMatrix Calculator With Steps
Explore matrix calculations with step-by-step mathematical explanations.
Open calculator
TOOL DIRECTORY
Explore the linear algebra toolkit
Browse planned tools by topic or search by name. Items marked “Coming Soon” are directory entries for future pages and are not currently available calculators.
Showing 207 of 207 planned tool listings.
Matrix Calculators
19 planned
tools
Matrix Division Calculator
Matrix Adjoint Calculator
Matrix Cofactor Calculator
Matrix Minor Calculator
Matrix Null Space Calculator
Matrix Column Space Calculator
Matrix Row Space Calculator
Matrix Diagonal Calculator
Matrix Symmetry Calculator
Matrix Equality Calculator
Matrix Square Calculator
Matrix Cube Calculator
Matrix Polynomial Calculator
Matrix Exponential Calculator
Matrix Logarithm Calculator
Matrix Modulo Calculator
Matrix Element Calculator
Matrix Size Calculator
Matrix Dimension Calculator
Linear Equation Solvers
17 planned
tools
Linear Equation Solver
Matrix Equation Solver
Ax=b Calculator
Gauss-Jordan Elimination Calculator
Reduced Row Echelon Form (RREF) Calculator
Row Echelon Form Calculator
Substitution Method Calculator
Elimination Method Calculator
Linear System Consistency Calculator
Homogeneous Equation Solver
Non-Homogeneous Equation Solver
Infinite Solution Calculator
Unique Solution Calculator
Linear Independence Calculator
Basis Calculator
Span Calculator
Vector Space Calculator
Eigenvalue & Eigenvector Tools
11 planned
tools
Eigenvalue Decomposition Calculator
Spectral Decomposition Calculator
Characteristic Equation Calculator
Eigenvalue Solver Step-by-Step
Eigenvector Normalization Calculator
Dominant Eigenvalue Calculator
Perron-Frobenius Calculator
Jordan Normal Form Calculator
Jordan Matrix Calculator
Algebraic Multiplicity Calculator
Geometric Multiplicity Calculator
Matrix Factorization Tools
11 planned
tools
LDU Decomposition Calculator
QR Decomposition Calculator
Cholesky Decomposition Calculator
Singular Value Decomposition (SVD) Calculator
Schur Decomposition Calculator
Polar Decomposition Calculator
Eigen Decomposition Calculator
Matrix Factorization Calculator
Low Rank Approximation Calculator
Rank Factorization Calculator
Nonnegative Matrix Factorization Calculator
Vector Calculators
19 planned
tools
Vector Addition Calculator
Vector Subtraction Calculator
Vector Multiplication Calculator
Vector Scalar Multiplication Calculator
Vector Magnitude Calculator
Vector Length Calculator
Unit Vector Calculator
Vector Projection Calculator
Vector Rejection Calculator
Vector Angle Calculator
Angle Between Vectors Calculator
Vector Normalization Calculator
Vector Orthogonalization Calculator
Gram-Schmidt Calculator
Vector Distance Calculator
Vector Similarity Calculator
Vector Direction Calculator
Vector Components Calculator
Vector Decomposition Calculator
Geometry & Transformation Tools
15 planned
tools
Matrix Transformation Calculator
Linear Transformation Calculator
Reflection Matrix Calculator
Scaling Matrix Calculator
Shear Matrix Calculator
Translation Matrix Calculator
2D Transformation Calculator
3D Transformation Calculator
Homogeneous Transformation Matrix Calculator
Coordinate Transformation Calculator
Change of Basis Calculator
Transformation Composition Calculator
Transformation Inverse Calculator
Affine Transformation Calculator
Projection Matrix Calculator
Statistics Matrix Tools
14 planned
tools
Correlation Matrix Calculator
Variance Matrix Calculator
Mean Vector Calculator
Standard Deviation Matrix Calculator
Scatter Matrix Calculator
Distance Matrix Calculator
Mahalanobis Distance Calculator
Confusion Matrix Calculator
Similarity Matrix Calculator
Adjacency Matrix Calculator
Kernel Matrix Calculator
Gram Matrix Calculator
Precision Matrix Calculator
Covariance Inverse Calculator
Machine Learning & AI Matrix Tools
20 planned
tools
Neural Network Calculator
Neural Network Forward Propagation Calculator
Neural Network Backpropagation Calculator
Weight Matrix Calculator
Bias Calculator
Activation Function Calculator
Softmax Calculator
Sigmoid Calculator
ReLU Calculator
Tanh Calculator
Cosine Similarity Calculator
Embedding Similarity Calculator
Vector Embedding Calculator
Attention Matrix Calculator
Transformer Attention Calculator
Query-Key-Value Calculator
Self-Attention Calculator
PCA Calculator
Principal Component Analysis Calculator
Feature Matrix Calculator
Calculus & Matrix Tools
10 planned
tools
Engineering Matrix Tools
14 planned
tools
Circuit Matrix Calculator
Electrical Network Matrix Calculator
Kirchhoff Matrix Calculator
Structural Matrix Calculator
Finite Element Matrix Calculator
Stiffness Matrix Calculator
Mass Matrix Calculator
Mechanical System Matrix Calculator
Control System Matrix Calculator
State Space Calculator
Transfer Matrix Calculator
Robot Transformation Matrix Calculator
Robotics Jacobian Calculator
Kinematics Matrix Calculator
Computer Science Matrix Tools
11 planned
tools
Matrix Generators & Utilities
17 planned
tools
Random Matrix Generator
Identity Matrix Generator
Zero Matrix Generator
Diagonal Matrix Generator
Symmetric Matrix Generator
Sparse Matrix Generator
Positive Definite Matrix Generator
Orthogonal Matrix Generator
Permutation Matrix Generator
Block Matrix Generator
Matrix Converter
Matrix Format Converter
CSV To Matrix Converter
JSON To Matrix Converter
Matrix To CSV Converter
Matrix To LaTeX Converter
Matrix LaTeX Generator
Educational Tools
11 planned
tools
Matrix Operation Explained
Linear Algebra Solver With Steps
Matrix Multiplication Steps
Determinant Steps Calculator
Inverse Matrix Steps Calculator
Eigenvalue Steps Calculator
Gaussian Elimination Steps
Interactive Matrix Lessons
Matrix Practice Generator
Linear Algebra Quiz Generator
Matrix Problem Generator
Visualization Tools
10 planned
tools
Advanced Research Tools
8 planned
tools
No planned tools match your search. Try a different term.
QUICK REFERENCE
A quick introduction to matrices
A matrix is a rectangular arrangement of numbers organized into rows and columns. Matrices are used to solve systems of equations, represent transformations, process data and model many scientific and engineering problems.
What are matrix dimensions?
A matrix with \(m\) rows and \(n\) columns is described as an \(m \times n\) matrix. Its dimensions determine which operations can be performed.
A = [ 1 2 3
4 5 6 ]
Dimensions: 2 × 3
This example has two rows and three columns. A square matrix has the same number of rows and columns.
Common matrix operations
- Addition and subtraction: corresponding entries are combined, and the matrices must have the same dimensions.
- Multiplication: the first matrix's column count must equal the second matrix's row count.
- Transpose: rows become columns and columns become rows.
- Determinant: a scalar associated with a square matrix.
- Inverse: a square matrix has an inverse only when it is nonsingular.
- Eigenvalues and eigenvectors: describe special directions and scaling factors for a linear transformation.
FREQUENTLY ASKED QUESTIONS
Matrix calculator FAQ
What can I calculate with an online matrix calculator?
Matrix calculators can perform operations such as addition, subtraction, multiplication, transposition, determinant calculation and matrix inversion. Other tools can address systems of equations, decompositions, vectors and transformations.
Can I multiply matrices with different dimensions?
Yes, provided the number of columns in the first matrix equals the number of rows in the second. For example, a 2 × 3 matrix can multiply a 3 × 4 matrix, producing a 2 × 4 matrix.
When does a matrix have an inverse?
A matrix must be square and nonsingular to have an inverse. Equivalently, its determinant must be nonzero.
Are all the tools in the directory available now?
No. The eight matrix operation pages at the top are listed as current tools. The other entries are planned pages and are marked “Coming Soon.” Their links use individual PHP filenames, but the corresponding pages must be created before they can provide a working calculator.
Who can use these matrix tools?
Students, teachers, researchers, programmers and professionals can use matrix calculators to check calculations, explore linear algebra concepts and support technical work. Always verify important results when using them for coursework or professional applications.