Matrix Addition Calculator
Add two matrices of compatible dimensions, element by element.
Open calculator
AVAILABLE CALCULATORS
Matrix calculators
Start with one of the available matrix operations below. Each calculator has its own page, so you can go directly to the calculation you need. This section updates automatically as new calculator files are installed.
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 Convergence Simulator
Explore matrix convergence, repeated transformations, and numerical behavior over successive iterations.
Open calculatorMatrix Power Calculator
Calculate nonnegative integer powers of a square matrix.
Open calculatorKronecker Product Calculator
Calculate the Kronecker product of two matrices.
Open calculatorMatrix Iteration Simulator
Explore repeated matrix multiplication and observe how vectors and matrices evolve over iterations.
Open calculatorMatrix Simulation Online
Explore interactive matrix operations, transformations, and numerical behavior through visual simulations.
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 calculatorEigenvalue and Eigenvector Simulator
Visualize eigenvalues, eigenvectors, and the geometric effects of matrix transformations.
Open calculatorMatrix Diagonalization Simulator
Explore matrix diagonalization and visualize how eigenvector bases simplify linear transformations.
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 calculatorLU Decomposition Simulator
Explore LU factorization and visualize lower and upper triangular matrix decomposition.
Open calculatorSVD Simulator
Visualize singular value decomposition and explore its applications in data analysis and machine learning.
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 calculatorGaussian Elimination Simulator
Follow Gaussian elimination step by step and visualize elementary row operations.
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 calculatorMatrix Transformation Simulator
Explore how matrices transform points, vectors, and geometric shapes in an interactive visual environment.
Open calculator2D Matrix Transformation Simulator
Visualize two-dimensional rotation, scaling, reflection, and shearing using transformation matrices.
Open calculator3D Matrix Transformation Simulator
Explore three-dimensional matrix transformations, rotations, scaling, and geometric projections.
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 calculatorMarkov Chain Simulator
Simulate state transitions, probability distributions, and long-run behavior in Markov chains.
Open calculatorRandom Walk Matrix Simulator
Explore random walks on graphs and networks using transition matrices and probability distributions.
Open calculatorPageRank Simulation Online
Simulate the PageRank algorithm and explore how link structures and damping affect page importance.
Open calculatorNeural Network Matrix Simulator
Explore how neural network layers use matrix multiplication, weights, biases, and activation functions.
Open calculatorMatrix Exponential Simulator
Explore matrix exponentials and simulate solutions to linear systems of differential equations.
Open calculatorControl System Matrix Simulator
Simulate engineering control systems using state-space matrices, input signals, and stability analysis.
Open calculatorMatrix Calculator With Steps
Explore matrix calculations with step-by-step mathematical explanations.
Open calculatorLinear Equation Solver
Open this calculator to perform linear equation solver calculations.
Open calculatorGauss-Jordan Elimination Calculator
Open this calculator to perform gauss-jordan elimination calculator calculations.
Open calculatorRow Echelon Form Calculator
Open this calculator to perform row echelon form calculator calculations.
Open calculatorLinear Independence Calculator
Open this calculator to perform linear independence calculator calculations.
Open calculatorBasis Calculator
Open this calculator to perform basis calculator calculations.
Open calculatorSpan Calculator
Open this calculator to perform span calculator calculations.
Open calculatorVector Addition Calculator
Open this calculator to perform vector addition calculator calculations.
Open calculatorVector Subtraction Calculator
Open this calculator to perform vector subtraction calculator calculations.
Open calculatorVector Magnitude Calculator
Open this calculator to perform vector magnitude calculator calculations.
Open calculatorUnit Vector Calculator
Open this calculator to perform unit vector calculator calculations.
Open calculatorVector Projection Calculator
Open this calculator to perform vector projection calculator calculations.
Open calculatorAngle Between Vectors Calculator
Open this calculator to perform angle between vectors calculator calculations.
Open calculatorVector Distance Calculator
Open this calculator to perform vector distance calculator calculations.
Open calculatorVector Components Calculator
Open this calculator to perform vector components calculator calculations.
Open calculatorCorrelation Matrix Calculator
Open this calculator to perform correlation matrix calculator calculations.
Open calculatorSoftmax Calculator
Open this calculator to perform softmax calculator calculations.
Open calculatorSigmoid Calculator
Open this calculator to perform sigmoid calculator calculations.
Open calculatorRandom Matrix Generator
Open this calculator to perform random matrix generator calculations.
Open calculatorIdentity Matrix Generator
Open this calculator to perform identity matrix generator calculations.
Open calculatorMatrix To LaTeX Converter
Open this calculator to perform matrix to latex converter calculations.
Open calculatorMatrix Multiplication Simulator
Open this calculator to perform matrix multiplication simulator calculations.
Open calculatorPower Iteration Simulator
Open this calculator to perform power iteration simulator calculations.
Open calculatorHadamard Product Calculator
Open this calculator to perform hadamard product calculator calculations.
Open calculator
TOOL DIRECTORY
Explore the linear algebra toolkit
Browse the complete collection of matrix and linear algebra tools. Available calculators are displayed above, while tools that are not yet installed are listed below by category. This directory updates automatically when new PHP files are added.
Showing 261 of 261 total tools.
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
11 planned
tools
Matrix Equation Solver
Ax=b Calculator
Reduced Row Echelon Form (RREF) Calculator
Substitution Method Calculator
Elimination Method Calculator
Linear System Consistency Calculator
Homogeneous Equation Solver
Non-Homogeneous Equation Solver
Infinite Solution Calculator
Unique Solution 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
11 planned
tools
Vector Multiplication Calculator
Vector Scalar Multiplication Calculator
Vector Length Calculator
Vector Rejection Calculator
Vector Angle Calculator
Vector Normalization Calculator
Vector Orthogonalization Calculator
Gram-Schmidt Calculator
Vector Similarity Calculator
Vector Direction 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
13 planned
tools
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
18 planned
tools
Neural Network Calculator
Neural Network Forward Propagation Calculator
Neural Network Backpropagation Calculator
Weight Matrix Calculator
Bias Calculator
Activation Function 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
Hessian Matrix Calculator
Gradient Matrix Calculator
Derivative Matrix Calculator
Differential Matrix Calculator
Matrix Function Calculator
Tensor Derivative Calculator
Multivariable Gradient Calculator
Vector Field Calculator
Divergence Calculator
Curl Calculator
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
Graph Matrix Calculator
Incidence Matrix Calculator
Laplacian Matrix Calculator
Transition Matrix Calculator
Cryptography Matrix Calculator
Hill Cipher Calculator
Image Matrix Calculator
Pixel Matrix Calculator
RGB Matrix Calculator
Convolution Matrix Calculator
Kernel Filter Calculator
Matrix Generators & Utilities
14 planned
tools
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 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
Matrix Heatmap Generator
Matrix Graph Visualizer
Eigenvector Visualizer
Eigenvalue Plotter
Matrix Transformation Visualizer
Vector Field Visualizer
3D Vector Visualizer
Linear Transformation Animator
Matrix Multiplication Visualization
Neural Network Matrix Visualization
Advanced Research Tools
7 planned
tools
Tensor Calculator
Tensor Decomposition Calculator
Spectral Norm Calculator
Matrix Stability Calculator
Positive Definite Test Calculator
Orthogonal Matrix Test Calculator
Sparse Matrix Calculator
No 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 × 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. Only tools whose corresponding PHP files exist on the server are displayed as available calculators. Other entries are listed as Coming Soon until their PHP files are created.
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.