Linear Algebra • Matrix Operations • AI • Engineering Math

About matrices.org

matrices.org is a comprehensive mathematics platform built around matrix operations, vector tools, linear equation solvers, eigenvalue and eigenvector calculators, factorization utilities, data science helpers, engineering mathematics tools, visualizers, generators, and step-by-step educational resources. The goal is to make matrix math easier, faster, clearer, and more searchable for students, teachers, engineers, researchers, and developers.

Matrix calculators Vector tools Linear algebra AI / ML utilities Educational explainers Visualizations
15
Main directories
240+
Tools and utilities
24/7
Accessible on desktop and mobile

What matrices.org is about

The site is designed as a specialized hub for matrix-related learning and computation. It combines practical calculators with theory, examples, and visual tools so users can solve problems, understand the formulas, and explore the structure of matrices from basic operations to advanced research topics.

Directories

The site is organized into 15 major directories covering the full matrix and linear algebra ecosystem.

Matrix Calculators

Starts at 1 and includes 30 tools
Matrix Calculator Matrix Addition Calculator Matrix Subtraction Calculator Matrix Multiplication Calculator Matrix Division Calculator Matrix Transpose Calculator Matrix Determinant Calculator Matrix Inverse Calculator Matrix Adjoint Calculator Matrix Cofactor Calculator Matrix Minor Calculator Matrix Trace Calculator Matrix Rank Calculator Matrix Null Space Calculator Matrix Column Space Calculator Matrix Row Space Calculator Matrix Diagonal Calculator Matrix Symmetry Calculator Matrix Equality Calculator Matrix Scalar Multiplication Calculator Matrix Power 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

Starts at 31 and includes 20 tools
Linear Equation Solver System of Equations Calculator Matrix Equation Solver Ax=b Calculator Gaussian Elimination Calculator Gauss-Jordan Elimination Calculator Reduced Row Echelon Form (RREF) Calculator Row Echelon Form Calculator Cramer's Rule 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

Starts at 51 and includes 15 tools
Eigenvalue Calculator Eigenvector Calculator Eigenvalue Decomposition Calculator Spectral Decomposition Calculator Characteristic Polynomial Calculator Characteristic Equation Calculator Eigenvalue Solver Step-by-Step Eigenvector Normalization Calculator Dominant Eigenvalue Calculator Perron-Frobenius Calculator Matrix Diagonalization Calculator Jordan Normal Form Calculator Jordan Matrix Calculator Algebraic Multiplicity Calculator Geometric Multiplicity Calculator

Matrix Factorization Tools

Starts at 66 and includes 12 tools
LU Decomposition Calculator 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

Starts at 78 and includes 22 tools
Vector Calculator Vector Addition Calculator Vector Subtraction Calculator Vector Multiplication Calculator Vector Scalar Multiplication Calculator Vector Magnitude Calculator Vector Length Calculator Unit Vector Calculator Dot Product Calculator Cross Product 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

Starts at 100 and includes 16 tools
Matrix Transformation Calculator Linear Transformation Calculator Rotation Matrix 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

Starts at 116 and includes 15 tools
Covariance Matrix Calculator 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

Starts at 131 and includes 20 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

Starts at 151 and includes 11 tools
Jacobian Matrix Calculator 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

Starts at 162 and includes 14 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

Starts at 176 and includes 14 tools
Graph Matrix Calculator Adjacency Matrix Calculator Incidence Matrix Calculator Laplacian Matrix Calculator PageRank Matrix Calculator Markov 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

Starts at 190 and includes 17 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

Starts at 207 and includes 12 tools
Matrix Calculator With Steps 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

Starts at 219 and includes 10 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

Starts at 229 and includes 12 tools
Tensor Calculator Tensor Decomposition Calculator Kronecker Product Calculator Hadamard Product Calculator Frobenius Norm Calculator Matrix Norm Calculator Spectral Norm Calculator Condition Number Calculator Matrix Stability Calculator Positive Definite Test Calculator Orthogonal Matrix Test Calculator Sparse Matrix Calculator

All tools with numbering

Every tool is listed below in the exact directory structure, with continuous numbering from 1 to 240.

1
Matrix Calculator
2
Matrix Addition Calculator
3
Matrix Subtraction Calculator
4
Matrix Multiplication Calculator
5
Matrix Division Calculator
6
Matrix Transpose Calculator
7
Matrix Determinant Calculator
8
Matrix Inverse Calculator
9
Matrix Adjoint Calculator
10
Matrix Cofactor Calculator
11
Matrix Minor Calculator
12
Matrix Trace Calculator
13
Matrix Rank Calculator
14
Matrix Null Space Calculator
15
Matrix Column Space Calculator
16
Matrix Row Space Calculator
17
Matrix Diagonal Calculator
18
Matrix Symmetry Calculator
19
Matrix Equality Calculator
20
Matrix Scalar Multiplication Calculator
21
Matrix Power Calculator
22
Matrix Square Calculator
23
Matrix Cube Calculator
24
Matrix Polynomial Calculator
25
Matrix Exponential Calculator
26
Matrix Logarithm Calculator
27
Matrix Modulo Calculator
28
Matrix Element Calculator
29
Matrix Size Calculator
30
Matrix Dimension Calculator
31
Linear Equation Solver
32
System of Equations Calculator
33
Matrix Equation Solver
34
Ax=b Calculator
35
Gaussian Elimination Calculator
36
Gauss-Jordan Elimination Calculator
37
Reduced Row Echelon Form (RREF) Calculator
38
Row Echelon Form Calculator
39
Cramer's Rule Calculator
40
Substitution Method Calculator
41
Elimination Method Calculator
42
Linear System Consistency Calculator
43
Homogeneous Equation Solver
44
Non-Homogeneous Equation Solver
45
Infinite Solution Calculator
46
Unique Solution Calculator
47
Linear Independence Calculator
48
Basis Calculator
49
Span Calculator
50
Vector Space Calculator
51
Eigenvalue Calculator
52
Eigenvector Calculator
53
Eigenvalue Decomposition Calculator
54
Spectral Decomposition Calculator
55
Characteristic Polynomial Calculator
56
Characteristic Equation Calculator
57
Eigenvalue Solver Step-by-Step
58
Eigenvector Normalization Calculator
59
Dominant Eigenvalue Calculator
60
Perron-Frobenius Calculator
61
Matrix Diagonalization Calculator
62
Jordan Normal Form Calculator
63
Jordan Matrix Calculator
64
Algebraic Multiplicity Calculator
65
Geometric Multiplicity Calculator
66
LU Decomposition Calculator
67
LDU Decomposition Calculator
68
QR Decomposition Calculator
69
Cholesky Decomposition Calculator
70
Singular Value Decomposition (SVD) Calculator
71
Schur Decomposition Calculator
72
Polar Decomposition Calculator
73
Eigen Decomposition Calculator
74
Matrix Factorization Calculator
75
Low Rank Approximation Calculator
76
Rank Factorization Calculator
77
Nonnegative Matrix Factorization Calculator
78
Vector Calculator
79
Vector Addition Calculator
80
Vector Subtraction Calculator
81
Vector Multiplication Calculator
82
Vector Scalar Multiplication Calculator
83
Vector Magnitude Calculator
84
Vector Length Calculator
85
Unit Vector Calculator
86
Dot Product Calculator
87
Cross Product Calculator
88
Vector Projection Calculator
89
Vector Rejection Calculator
90
Vector Angle Calculator
91
Angle Between Vectors Calculator
92
Vector Normalization Calculator
93
Vector Orthogonalization Calculator
94
Gram-Schmidt Calculator
95
Vector Distance Calculator
96
Vector Similarity Calculator
97
Vector Direction Calculator
98
Vector Components Calculator
99
Vector Decomposition Calculator
100
Matrix Transformation Calculator
101
Linear Transformation Calculator
102
Rotation Matrix Calculator
103
Reflection Matrix Calculator
104
Scaling Matrix Calculator
105
Shear Matrix Calculator
106
Translation Matrix Calculator
107
2D Transformation Calculator
108
3D Transformation Calculator
109
Homogeneous Transformation Matrix Calculator
110
Coordinate Transformation Calculator
111
Change of Basis Calculator
112
Transformation Composition Calculator
113
Transformation Inverse Calculator
114
Affine Transformation Calculator
115
Projection Matrix Calculator
116
Covariance Matrix Calculator
117
Correlation Matrix Calculator
118
Variance Matrix Calculator
119
Mean Vector Calculator
120
Standard Deviation Matrix Calculator
121
Scatter Matrix Calculator
122
Distance Matrix Calculator
123
Mahalanobis Distance Calculator
124
Confusion Matrix Calculator
125
Similarity Matrix Calculator
126
Adjacency Matrix Calculator
127
Kernel Matrix Calculator
128
Gram Matrix Calculator
129
Precision Matrix Calculator
130
Covariance Inverse Calculator
131
Neural Network Calculator
132
Neural Network Forward Propagation Calculator
133
Neural Network Backpropagation Calculator
134
Weight Matrix Calculator
135
Bias Calculator
136
Activation Function Calculator
137
Softmax Calculator
138
Sigmoid Calculator
139
ReLU Calculator
140
Tanh Calculator
141
Cosine Similarity Calculator
142
Embedding Similarity Calculator
143
Vector Embedding Calculator
144
Attention Matrix Calculator
145
Transformer Attention Calculator
146
Query-Key-Value Calculator
147
Self-Attention Calculator
148
PCA Calculator
149
Principal Component Analysis Calculator
150
Feature Matrix Calculator
151
Jacobian Matrix Calculator
152
Hessian Matrix Calculator
153
Gradient Matrix Calculator
154
Derivative Matrix Calculator
155
Differential Matrix Calculator
156
Matrix Function Calculator
157
Tensor Derivative Calculator
158
Multivariable Gradient Calculator
159
Vector Field Calculator
160
Divergence Calculator
161
Curl Calculator
162
Circuit Matrix Calculator
163
Electrical Network Matrix Calculator
164
Kirchhoff Matrix Calculator
165
Structural Matrix Calculator
166
Finite Element Matrix Calculator
167
Stiffness Matrix Calculator
168
Mass Matrix Calculator
169
Mechanical System Matrix Calculator
170
Control System Matrix Calculator
171
State Space Calculator
172
Transfer Matrix Calculator
173
Robot Transformation Matrix Calculator
174
Robotics Jacobian Calculator
175
Kinematics Matrix Calculator
176
Graph Matrix Calculator
177
Adjacency Matrix Calculator
178
Incidence Matrix Calculator
179
Laplacian Matrix Calculator
180
PageRank Matrix Calculator
181
Markov Matrix Calculator
182
Transition Matrix Calculator
183
Cryptography Matrix Calculator
184
Hill Cipher Calculator
185
Image Matrix Calculator
186
Pixel Matrix Calculator
187
RGB Matrix Calculator
188
Convolution Matrix Calculator
189
Kernel Filter Calculator
190
Random Matrix Generator
191
Identity Matrix Generator
192
Zero Matrix Generator
193
Diagonal Matrix Generator
194
Symmetric Matrix Generator
195
Sparse Matrix Generator
196
Positive Definite Matrix Generator
197
Orthogonal Matrix Generator
198
Permutation Matrix Generator
199
Block Matrix Generator
200
Matrix Converter
201
Matrix Format Converter
202
CSV To Matrix Converter
203
JSON To Matrix Converter
204
Matrix To CSV Converter
205
Matrix To LaTeX Converter
206
Matrix LaTeX Generator
207
Matrix Calculator With Steps
208
Matrix Operation Explained
209
Linear Algebra Solver With Steps
210
Matrix Multiplication Steps
211
Determinant Steps Calculator
212
Inverse Matrix Steps Calculator
213
Eigenvalue Steps Calculator
214
Gaussian Elimination Steps
215
Interactive Matrix Lessons
216
Matrix Practice Generator
217
Linear Algebra Quiz Generator
218
Matrix Problem Generator
219
Matrix Heatmap Generator
220
Matrix Graph Visualizer
221
Eigenvector Visualizer
222
Eigenvalue Plotter
223
Matrix Transformation Visualizer
224
Vector Field Visualizer
225
3D Vector Visualizer
226
Linear Transformation Animator
227
Matrix Multiplication Visualization
228
Neural Network Matrix Visualization
229
Tensor Calculator
230
Tensor Decomposition Calculator
231
Kronecker Product Calculator
232
Hadamard Product Calculator
233
Frobenius Norm Calculator
234
Matrix Norm Calculator
235
Spectral Norm Calculator
236
Condition Number Calculator
237
Matrix Stability Calculator
238
Positive Definite Test Calculator
239
Orthogonal Matrix Test Calculator
240
Sparse Matrix Calculator

Contact

For support, corrections, content requests, partnerships, or tool suggestions, email the site administrator at admin@matrices.org.

Email admin

Mission

matrices.org aims to become a complete matrix knowledge and utility platform: a place where users can calculate, verify, visualize, compare, and learn every major matrix and vector concept in one clean, mobile-friendly interface.