Matrix Solver Step by Step vs Linear Algebra Visualizer

“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.

Ever wondered what a matrix is really doing? Whether you're learning it yourself or teaching students who are stuck, this app lets you visualise and manipulate matrix transformations, so you can finally see how and why they work. WHY IT CLICKS Most apps show you the answer. This one shows you why. The columns of a matrix are just where the basis vectors î and ĵ land. Column one is red. Column two is green. Follow those colors from your input, through the transformed vectors, into the step-by-step math. One number, traced all the way to its effect. With Linear Algebra Visualizer you: - Can finally build the visual intuition of linear algebra - Understand the math behind each transformation - Visually see why TRS order matters - Understand the effect of adding multiple matrices and translations - Watch eigenvectors and eigenvalues come alive BUILT FOR - Students surviving their first linear algebra course - Graphics programmers who want intuition, not just formulas - Teachers who need a live demo that lands - Anyone who's stared at a matrix and thought "but why does this work?" - Visual thinkers who've struggled to picture it all in their head Stop memorizing matrices. Start seeing them. Download Linear Algebra Vizualiser: Rotate, Scale, Shear, Reflect, Translate and learn to understand transformations visually. Ever wondered what a matrix is really doing? Whether you're learning it yourself or teaching students who are stuck, this app lets you visualise and manipulate matrix transformations, so you can finally see how and why they work. WHY IT CLICKS Most apps show you the answer. This one shows you why. The columns of a matrix are just where the basis vectors î and ĵ land. Column one is red. Column two is green. Follow those colours from your input, through the transformed vectors, into the step-by-step math. One number, traced all the way to its effect. With Linear Algebra Visualiser you: - Can finally build the visual intuition of linear algebra - Understand the math behind each transformation - Visually see why TRS order matters - Understand the effect of adding multiple matrices and translations - Watch eigenvectors and eigenvalues come alive BUILT FOR - Students surviving their first linear algebra course - Graphics programmers who want intuition, not just formulas - Teachers who need a live demo that lands - Anyone who's stared at a matrix and thought "but why does this work?" - Visual thinkers who've struggled to picture it all in their head Stop memorising matrices. Start seeing them. Download Linear Algebra Visualiser: Rotate, Scale, Shear, Reflect, Translate and learn to understand transformations visually. Terms of Use (EULA): https://www.apple.com/legal/internet-services/itunes/dev/stdeula/