Matrix Solver Step by Step vs Galton Board App

“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.

Unlock the power of probabilities and explore the beauty of mathematics in motion with the Galton Board App. This innovative application transforms your mobile device into a dynamic, interactive probability demonstrator that brings centuries-old mathematical concepts to life. The app utilizes your iPhone's and iPad's gyroscope capabilities, creating an immersive experience where the beads appear as if they are rolling around inside your device. The Galton Board was invented by Sir Francis Galton in 1873 to illustrate the binomial distribution. Through our app, we've recreated this educational tool to demonstrate how, with a large number of beads and rows of hexagons, it approximates the normal distribution - a concept known as the Central Limit Theorem. Key Features: • An interactive Galton Board that displays the principles of probabilities and the binomial distribution. • Detailed explanations of related mathematical concepts, including probability theories, independent identically distributed (IID) random variables, regression to the mean, the law of large numbers, the random walk, the Gambler's Fallacy, and more. • A "Stock Market Data" version, simulating the probabilities of a range of historical monthly market returns, and demonstrating their correlation with the binomial distribution. • The 'Historical Monthly Return Beads' featured with the Stock Market Data, where beads fall through the board based on monthly historical returns for a choice of 20 index portfolios. • Pause or slow-motion options to study the bead movement and distribution patterns in detail. The Galton Board App is ideal for statistics, math, and stock market enthusiasts. It is not just an app, it's an immersive, hands-on approach to understanding probabilities, the binomial distribution, and the stock market behavior. Presented by Index Fund Advisors, this app is your go-to educational tool. Download now and embark on a fascinating journey into the world of probabilities and the "law of unreason" as referred to by Sir Francis Galton himself!