Matrix Solver Step by Step vs Linear Algebra

“Matrix Solver Step by Step” Linear Algebra learning tool and a Matrix Calculator: * Performs most commonly used matrix calculations and decompositions (see list below). * Demonstrates and explains algorithm steps for almost all the functions. * Draws interactive geometric references when appropriate. * Provides tutorials (explanations and proofs) for most Linear Algebra concepts. The tutorial topics have links to all other relevant topics, making them understandable for users with minimal prior knowledge of Linear Algebra. Every effort is being made to ensure user friendly interface and factual accuracy. The app is, so far, free of charge and free of ads. It is being continuously updated with new functions, graphs, and proofs. Suggestions and corrections are welcome! Write to us at graphmath@aol.com. List of functions (matrix size up to 8x8): 1. Solution for linear systems, real and complex. 2. Geometric solutions for 3 equation linear systems. 3. Matrix multiplication. 4. Matrix inverse, real and complex. 5. Determinant (row reduction, recursive and permutations methods). 6. Eigenvectors and eigenvalues, both real and complex. 7. Diagonalization. 8. Rotation-scaling similarity transformation. 9. Block-diagonalization transformation. 10. PLU factorization for square matrices. 11. LD(L transposed) factorization for symmetric matrices. 12. Column-Row factorization. 13. QR factorization by 3 existing methods: Gram-Schmidt, Givens rotations and Householder reflections. 14. Singular Value Decomposition (SVD), including using of SVD for Image compression. 15. Polar factorization. 16. Interactive graphs for transformation by 2x2 and 3x3 matrices, with derivation of specific matrix types, such as rotation or reflection. 17. Raising a Matrix to power n, where n is any integer between -10 and 10. 18. Matrix exponentials, x = exp(A*t) * x0. 19. Markov chain calculator. 20. Calculation of Correlation matrices and Principal Component Analysis (PCA). UI features: Most recent matrix entry for particular operation and size is saved between program runs. Input or output matrices can be saved to clipboard and pasted into other input screens in the app, text files and spreadsheets. Matrix and Linear Equations entries can be saved into table and are available after application is closed and re opened. Matrix entries can be filled with random numbers, different options for range are provided. Solutions as fractions are available for many functions. Eigenvalues and eigenvectors are shown as fractions and radicals for 2x2 matrices. Tutorial items can be saved into "My Tutorial Chapters" list. Comments can be added to most tutorial chapters and saved into "My Comments" list.

Linear Algebra - Matrix Solver is a powerful and easy-to-use tool for calculating matrices, determinants, and vector operations — perfect for students, engineers, and anyone who works with linear algebra in study or professional tasks. The app performs step-by-step calculations with detailed solutions using the correct formulas. You can work with matrices up to 5×5 and vectors in 2D or 3D. Each calculator includes a brief theoretical overview to help you understand the concept behind the operation. It also includes a random number generator to instantly create practice problems with random values. Available in 8 languages: English, French, German, Italian, Portuguese, Spanish, Russian, Ukrainian. Whether you're learning, teaching, or solving real-world problems, Linear Algebra app helps you get accurate results quickly and understand the math behind them. The application perform following operations with matrices: • Matrix addition • Matrix subtraction • Matrix scalar multiplication • Matrix square • Matrix multiplication • Matrix transposition Determinant calculations: • Calculation of the determinant using the Sarrus method • Calculation of the determinant using the Laplace method Vector operations: • Vector Length • Vector coordinates by two points • Vectors addition • Vectors subtraction • Scalar and vector multiplication • Scalar product of vectors • Cross product of vectors • Mixed (scalar) triple product • Angle between two vectors • Projection of a vector onto another vector • Direction cosines • Collinear vectors • Orthogonal vectors • Coplanar vectors • Area of triangle formed by vectors • Area of a parallelogram formed by vectors • Volume of pyramid formed by vectors • Volume of a parallelepiped formed by vectors Download now and simplify your linear algebra work!