Algorithms HQ vs Matrix Solver Step by Step

A fun and didactic app to learn computer science algorithms! See how algorithms are working by watching an animation of their execution. Understand how data is manipulated as it is animated through an intuitive representation of its contents. Always know which line is executed in the pseudo-code, what are the values of the variables. Need to quickly refresh your memory? Just use the app as a quick reference on the main characteristics of each algorithm! Main features: - Execute a single instruction, or undo the previous one - Run, or rewind the algorithm until you decide to pause the execution - Adjust the speed of the animation - Best and worst case input data for sorting algorithms - Change the input data: size (up to 500), maximum value or data distribution (random, sorted, many duplicates, etc.) - For data structures, choose the next function to execute, or let a scenario choose for you, so you can see how the data structure evolves. - Landscape or portrait orientation This version contains the following algorithms: Linear Data Structures: - Linked Lists, including a view on memory - Queue - Stack Sorting algorithms: - Bubble Sort - Cocktail Sort - Gnome Sort - Insertion Sort - Quick Sort - Selection Sort More algorithms and more features are on the way!

“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.