Matrix Solver Step by Step vs Terramoto

“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.

Terramoto brings the science of earthquakes and tsunamis to life with stunning real-time physics simulation. DISCLAIMER This app is for educational and entertainment purposes only. Terramoto is NOT an emergency warning system and should NOT be used for disaster planning, evacuation decisions, or any life-safety purposes. The simulations are simplified models that do not account for all real-world factors. For actual tsunami warnings, always rely on official sources such as NOAA, local emergency management agencies, and government alerts. REAL PHYSICS, NOT ANIMATIONS Unlike simple visualizations, Terramoto uses actual shallow water equations—the same mathematics used by scientific institutions—to simulate how tsunami waves propagate across oceans. Watch waves travel at realistic speeds, reflect off coastlines, and flood coastal areas based on real elevation data. GPU-ACCELERATED SIMULATION Powered by Metal compute shaders, Terramoto runs a full fluid dynamics simulation on your device. The well-balanced hydrostatic solver ensures physically accurate wave behavior without artificial artifacts. GLOBAL COVERAGE Accurate coastlines from Natural Earth public domain data Real bathymetry (ocean depth) affecting wave speed and behavior Waves travel faster in deep ocean, slow and amplify in shallow coastal waters AFFECTED CITIES ANALYSIS See which cities would be impacted by seismic events. Terramoto calculates distances and provides estimates based on magnitude and proximity. FEATURES Tap anywhere on the map to simulate earthquakes of varying magnitudes Watch tsunami waves propagate in real-time across the globe Observe wave reflection, refraction, and coastal flooding Track simulation time and wave progression Smooth, interpolated wave visualization Dark mode interface designed for clarity EDUCATIONAL VALUE Perfect for students, educators, and anyone curious about geophysics. Understand why some coastlines are more vulnerable to tsunamis, how ocean depth affects wave speed, and why early warning systems are critical.