Matrix Solver Step by Step vs Calculus

“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.

Study Calculus from A to Z in 10 chapters, all in one app! Then play the in-app Calculus Quiz game to perfect your skills. One Level builds the necessary knowledge for the next Level as you advance. - Suitable for BEGINNERS: Teach yourself Calculus from Zero to the level of a Pro using the HINTS provided. - Adequate for the PROs: Revise and consolidate your Calculus knowledge while facing off with real Pure Math challenges. - Enjoy crisp clear Math text that adjusts its Font size and adapts to both Light and Dark Mode. Featured topics: - Differentiation 1: Curve gradient, Tangents and Normals, Velocity and Acceleration - Differentiation 2: Maxima and Minima, Curve sketching, Second derivative, Small changes - Integration: Reverse differentiation, Area under a curve, Definite integrals, Solids of Revolution, Centres of gravity - Further differentiation: Chain rule, Products and Quotients, Implicit functions, Parameters, Second derivatives - Trigonometry: Radian measure, Trigonometry derivatives, Inverse trigonometry, General solutions - Further Integration 1: Function and derivative, Change of variable, Parameters, Inverse trigonometry - Exponential and Log functions: The exponential function, Deriving y = e^x, The natural logarithm, Logarithmic differentiation - Partial fractions: Linear factors, Quadratic factors, Repeated roots, Improper fractions - Further Integration 2: Integration by parts, Taking dv/dx as 1, Variable t = tan(x/2), Splitting the numerator - Differential equations: Separating variables, Integrating factor, Homogenous equations, Differential problems