Matrix Calculators

Matrix Rank Calculator

Compute rank for 2x2 and 3x3 matrices via RREF

Adjugate Matrix Calculator

Compute adjugate via minors and cofactors for 2x2 and 3x3

Inverse Matrix Calculator

Compute the inverse via adjugate method for 2x2 and 3x3

Eigenvalue Calculator

Find eigenvalues via characteristic equation for 2x2 and 3x3

Linear System Solver

Solve Ax=b using Cramer rule for 2x2 and 3x3 systems

Determinant Calculator

Compute determinants for 2x2 and 3x3 matrices step by step

Matrix Null Space Calculator

Find basis for null space (kernel) of Ax=0 via RREF

Matrix Column Space Calculator

Find basis for column space using pivot columns from RREF

Matrix Row Space Calculator

Find basis for row space using non-zero rows from RREF

Left Null Space Calculator

Find left null space basis via transpose and RREF

Vector Basis Calculator

Check linear independence and find basis for a set of vectors

Matrix Characteristic Polynomial Calculator

Compute det(A-λI) for 2x2 and 3x3 matrices with detailed step-by-step derivation

Cholesky Decomposition Calculator

Compute A = LLᵀ where L is lower triangular with positive diagonal entries

Congruent Matrix Checker

Determine if two matrices are congruent (A ≃ B) by checking if B = PᵀAP

Hermitian Matrix Checker

Verify if A = A* (Hermitian) with detailed step-by-step verification

Idempotent Matrix Checker

Verify if A² = A (idempotent matrix) with detailed step-by-step verification

Involutory Matrix Checker

Verify if A² = I (self-inverse matrix) with detailed step-by-step computation

Jordan Canonical Form Calculator

Transform matrices to Jordan normal form with detailed step-by-step derivation

Linear Dependence Checker

Test if vectors are linearly dependent or independent with detailed rank and determinant analysis

Matrix Logarithm Calculator

Compute log(I+A) for 2x2 matrices using Taylor series expansion

LU Decomposition Calculator

Compute A = LU where L is lower triangular and U is upper triangular

Matrix Minimal Polynomial Calculator

Find the monic polynomial of least degree annihilating a matrix

Nilpotent Matrix Checker

Verify if matrix is nilpotent (A^k = 0 for some k) with detailed computation

Projection Matrix Calculator

Compute orthogonal projection matrices and projected vectors in 2D and 3D space

Moore-Penrose Pseudoinverse Calculator

Compute A⁺ (pseudoinverse) using SVD method with detailed step-by-step computation

QR Decomposition Calculator

Compute A = QR where Q is orthogonal and R is upper triangular

Schur Decomposition Calculator

Compute A = QUQ⁻¹ with unitary Q and upper triangular U

Similar Matrix Checker

Determine if two matrices are similar (A ~ B) by checking eigenvalues, trace, determinant, and rank

Skew-Hermitian Matrix Checker

Verify if A = -A* (anti-Hermitian) with detailed step-by-step verification

SVD Decomposition Calculator

Compute singular value decomposition A = UΣV* with detailed step-by-step computation

Unitary Matrix Checker

Verify if a matrix is unitary (U*U = UU* = I) with detailed verification

Gram-Schmidt Orthogonalization Calculator

Compute orthogonal basis using Gram-Schmidt process for 2D and 3D vectors

Orthonormal Basis Generator

Generate orthonormal basis with Gram-Schmidt and normalization for 2D and 3D vectors

Matrix Trace Calculator

Compute trace (sum of diagonal elements) for 2x2 and 3x3 matrices

Matrix Power Calculator

Compute A^n by repeated matrix multiplication for 2x2 and 3x3 matrices

Matrix Exponential Calculator

Compute e^A using Taylor series for 2x2 and 3x3 matrices

Matrix Transpose Calculator

Find A transpose by swapping rows and columns for 2x2 and 3x3 matrices

Matrix Addition Calculator

Add two matrices entry by entry for 2x2 and 3x3 matrix inputs

Matrix Subtraction Calculator

Subtract two matrices entry by entry for 2x2 and 3x3 matrix inputs

Matrix Multiplication Calculator

Multiply two matrices using row by column products for 2x2 and 3x3 inputs

Scalar Matrix Multiplication Calculator

Multiply every matrix entry by a scalar value for 2x2 and 3x3 matrices

Diagonal Matrix Checker

Check whether all off-diagonal entries are zero in a square matrix