Matrix Solver Step by Step26.10 - App Store

“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.

Version History Bug fixes, crash prevention 26.10 12/18/2025 Added link to our new app, Discrete Probability (calculator, proofs, graphs). 26.9 11/06/2025 Bug fix. 26.8.1 09/15/2025 UI improvements. 26.8 08/11/2025 Bug fix, crash prevention. 26.7.1 08/10/2025 UI improvements in the new Matrix Multiplication Tutorial. 26.7 07/10/2025 New Matrix Multiplication Tutorial 26.6 07/08/2025 Calculation of parametric solution set with explanation. 26.5 07/03/2025 Added links to our new app, 'Math Editor', which is a tool to create Math (including Linear Algebra) notes, posters and presentations. 26.4 04/25/2025 Fixed an issue with e-mail not sending from "About / Contact us" section. 26.3 04/05/2025 Minor improvements 26.2.3 03/19/2025 Bug fix 26.2.2 03/13/2025 Minor code changes 26.2.1 03/11/2025 New app icon, UI improvements, bug fix. 26.2 03/06/2025 1. More efficient and realistic drawing of equations as 3D planes.
2. Other UI improvements and bug fixes. 26.1 02/10/2025 1. Search for calculator functions.
2. UI improvements 26.0 02/05/2025 UI improvements.
(Link to our new app, "Construct Polynomial: Interpolate and Approximate", was added in previous version 25.1) 25.2 02/05/2025 1. Link to our new app, "Construct Polynomial: Interpolate and Approximate".
2. UI improvements and bug fixes. 25.1 02/04/2025 UI and performance improvements. 25.0 02/02/2025 Fixed issue with delayed response of Home Screen buttons. 24.29 01/16/2025 1. Links to our new app, 'Polynomial Solver\nStep by Step', which will replace 'Polynomials and\nLinear Systems'.
2. Minor improvements. 24.28 11/16/2024 Improved eigenvalue calculation algorithm. 24.27 11/06/2024 Tutorial improvements. 24.26 10/27/2024 Tutorial improvements, bug fix. 24.25 10/20/2024 1. Link to our new app: 'Calcu-Logarithm', all about logarithms, from Arithmetic to Calculus.
2. Minor changes and bug fixes. 24.24 09/22/2024