Matrix Solver Step by Step vs Art of Stat

“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.

Bootstrap Confidence Intervals and Permutation Tests for Means, Medians, Proportions, the Correlation Coefficient and the Slope, and the Chi-Square Test for Independence. Modern statistical calculator for teachers and students of statistics. The Art of Stat: Resampling app lets you find bootstrap confidence intervals and permutation P-values. The app illustrates the procedures interactively so you can understand how they work. Several example datasets are preloaded for you to explore, but you can also enter your own data or import a CSV file. The following resampling methods are implemented: - Bootstrap Confidence Interval for a population mean, median, or standard deviation. - Bootstrap Confidence Interval for a population proportion or the population odds. - Bootstrap Confidence Interval for a population correlation (Pearson and Spearman) or the population slope of a regression model. - Bootstrap Confidence Interval for the difference of two population means or medians. - Permutation Test for a population mean or median. - Permutation Test for the difference of two population means or medians. - Permutation Test for the independence of two categorical variables (Permutation Chi-Squared Test) Easily find the bootstrap confidence interval based on the percentile and other methods. For inference about population means, compare results to traditional methods based on the Student-t distribution. For the Chi-squared test of independence, compare to the results from Pearson's Chi-squared test. Each procedure has three screens: 1) Enter Data on the first screen in various ways, and obtain descriptive statistics and corresponding graphs (Histogram, Boxplot, Bar Chart). 2) Generate the bootstrap or permutation distribution on the second screen, step-by-step, or 1,000 at a time. 3) Obtain the Bootstrap Confidence Interval or Permutation P-value on the third screen, along with lots of supporting information and comparison to classical, central-limit-based inference. The app comes with several example datasets pre-loaded, but you can also upload your own .CSV file or create one in the Data Editor. Easily share results by taking screenshots. Unlock all content for a one-time small fee!