Starlight Tools

Starlight Tools directory

Linear Algebra & Matrix Calculators

25 free, browser-based tools. No account required.

Work with vectors, matrices, and coordinate transformations using private browser-based linear algebra tools. Start with the LU Decomposition Calculator, Vector Projection Calculator, or Transformation Matrix Calculator.

Yellow star mascot projecting one vector onto another

Vector Projection, Dot & Cross Product

Calculate projection, rejection, dot product, cross product, angle, magnitude, and area with steps. v1.0.0

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Yellow star mascot calculating the cross product of two 3D vectors

Cross Product Calculator for 3D Vectors

Calculate A × B with determinant steps, magnitude, unit normal, angle, areas, and perpendicularity checks. v1.0.0

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Yellow star mascot resolving a vector into horizontal and vertical components

Vector Component Resolver

Resolve 2D or 3D vectors into components or recover magnitude, azimuth, and elevation. v1.0.0

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Yellow star mascot measuring the angle between two vectors

Angle Between Two Vectors

Find the angle, dot product, magnitudes, and cosine similarity for 2D, 3D, or 4D vectors. v1.0.0

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Coordinate transformation tool applying translation rotation reflection and scale

Coordinate Transformations

Translate, rotate, reflect, and scale one or many 2D points with matrices and a live preview. v1.0.0

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2D rotation matrix calculator building a matrix and rotating points

2D Rotation Matrix Calculator

Build a rotation matrix, rotate points around any center, or extract an angle from a matrix. v1.0.0

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Transformation matrix calculator composing translation rotation scale and reflection

Geometric Transformation Matrix

Compose ordered 2D transformations into one 3×3 matrix and apply it to points. v1.0.0

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LU decomposition calculator showing lower-triangular and upper-triangular matrix factors

LU Decomposition Calculator

Factor a square matrix with partial pivoting and follow every P, L, and U step. v1.0.0

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Yellow star mascot demonstrating a Cholesky matrix decomposition

Cholesky Decomposition Calculator

Factor a symmetric positive-definite matrix into L and Lᵀ with entry-by-entry steps and an accuracy check. v1.0.0

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Gram–Schmidt calculator transforming skewed vectors into perpendicular unit vectors

Gram–Schmidt Orthonormalization Calculator

Build an orthonormal basis with projection steps, Q and R matrices, and numerical checks. v1.0.0

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Yellow star mascot demonstrating a QR matrix decomposition

QR Decomposition Calculator

Factor a square or tall matrix with Householder steps, Q and R matrices, rank, and accuracy checks. v1.0.0

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Yellow star mascot demonstrating a singular value decomposition

Singular Value Decomposition Calculator

Factor tall, square, or wide matrices into U, Σ, and Vᵀ with Jacobi steps, singular values, rank, and accuracy checks. v1.0.0

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Yellow star mascot measuring matrix sensitivity and numerical stability

Matrix Condition Number Calculator

Measure numerical stability using the 2, 1, infinity, or Frobenius norm, with singular values and rank diagnostics. v1.0.0

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Yellow star mascot calculating matrix rank and nullity

Matrix Rank and Nullity Calculator

Find rank, nullity, RREF, pivot and free columns, and bases for the null, column, and row spaces. v1.0.0

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Yellow star mascot identifying independent vectors and a basis

Linear Independence and Basis Calculator

Test vectors for independence, extract a basis for their span, and see RREF and dependence relations. v1.0.0

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Yellow star mascot comparing a matrix null space and column space

Null Space and Column Space Calculator

Find null-space and column-space bases, dimensions, RREF, pivot and free columns, and verification. v1.0.0

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Yellow star mascot demonstrating matrix addition multiplication and transpose

Matrix Calculator

Add, multiply, or transpose matrices up to 8×8 with dimension checks, working steps, and export controls. v1.0.0

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A determinant calculator expanding a 3 by 3 matrix into signed 2 by 2 minors

Determinant Calculator

Calculate 2×2 to 5×5 determinants with a complete step-by-step cofactor expansion. v1.0.0

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A matrix scaling an eigenvector in the same direction by its eigenvalue

Eigenvalue and Eigenvector Calculator

Find real or complex eigenvalues, eigenspace bases, multiplicities, and verification steps for 2×2 and 3×3 matrices. v1.0.0

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Yellow star mascot demonstrating matrix diagonalization

Matrix Diagonalization Calculator

Find P, D, and P⁻¹ over the real or complex numbers, with eigenspace, defect, and reconstruction steps. v1.0.0

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An augmented matrix transforming from A beside I into I beside the inverse

Inverse Matrix Calculator

Invert 2×2 to 6×6 matrices with scaled pivoting and every Gauss–Jordan row operation. v1.0.0

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Yellow star mascot converting vector coordinates between two bases

Change of Basis Matrix Calculator

Convert coordinates between two ordered bases, calculate both change matrices, and verify an optional vector. v1.0.0

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Linear algebra matrix being reduced to row echelon form

Row Reduction Calculator

Reduce rectangular or augmented matrices to REF or RREF with complete row-operation steps, rank, and pivot columns. v1.0.0

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Yellow star mascot solving a linear system by row reduction

System of Linear Equations Solver

Solve 2–8 equations with Gaussian elimination, solution classification, and complete row-operation steps. v1.0.0

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Yellow star mascot fitting a least-squares regression line

Least Squares Regression Matrix Calculator

Fit y ≈ Xβ with an SVD pseudoinverse, coefficients, predictions, residuals, R², RMSE, rank, and matrix steps. v1.0.0

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About These Linear Algebra Tools

These tools cover vector operations and matrix-based transformations with numerical results, visual explanations, and working steps. They run locally and support common classroom, graphics, engineering, and data applications.