Shelvean Kapita

Interactive Linear Algebra Tools

Explore fundamental concepts in linear algebra through interactive JavaScript visualizations and calculators. Enter matrices and adjust parameters in real time.

Geometry of Linear Systems

Visualize the row and column pictures for 2D linear systems.

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Matrix Product

Interactive computation and visualization of matrix multiplication as composition of linear transformations.

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Determinant and Trace

Compute the determinant and trace of small matrices using elementary matrix operations.

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Reduced Row Echelon Form Solver (RREF)

Step-by-step Gauss-Jordan elimination to compute the reduced row echelon form.

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Matrix Inverse

Compute the inverse of a square matrix via augmented row reduction.

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Elementary Matrices

Explore how elementary row operations are represented by multiplication by elementary matrices.

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Row Echelon Form Solver (REF)

Perform Gaussian elimination to compute the row echelon form.

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Change of Coordinates (Transition Matrix)

Convert vector coordinates between bases using the transition matrix.

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Similarity Transforms

Find the matrix representation of a linear operator.

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Gram Schmidt Orthogonalization

Apply the Gram-Schmidt process to obtain an orthogonal (or orthonormal) basis step-by-step.

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Matrix Diagonalization

Diagonalize a matrix using its eigenvectors when possible.

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Cholesky Factorization

Compute the Cholesky decomposition for symmetric positive definite matrices.

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Four Fundamental Subspaces

Compute bases for the column space, null space, row space, and left null space of a matrix.

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A = CR Factorization

Compute the rank-revealing factorization of a matrix.

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Magic Factorization

Compute the rank-revealing factorization of a matrix.

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Linear Equation Solver

Solve a linear system with detailed step-by-step row reduction.

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Matrix Inverse or Pseudo-Inverse

Compute the inverse (if it exists) or the Moore-Penrose pseudo-inverse.

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PA = LU Factorization

Compute the LU decomposition with partial and scaled partial pivoting.

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QR Factorization

Compute the orthogonal-triangular decomposition.

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Least Squares Solver using QR Factorization

Solve the least squares problem using QR decomposition.

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Least Squares Solver using Normal Equations

Solve the least squares problem using the normal equations.

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Least Squares Solver using SVD

Solve the least squares problem using singular value decomposition.

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Eigenvalues and Eigenvectors

Compute eigenvalues and eigenvectors.

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Singular Value Decomposition (SVD)

Compute the full singular value decomposition.

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