Matrix Solver Step by Step 24.16.1

Matrix Solver Step by Step is a comprehensive linear algebra learning tool and matrix calculator that offers a wide range of functionalities:

• Performs various matrix calculations and decompositions including solutions for linear systems, matrix multiplication, matrix inverse, determinants, eigenvectors, eigenvalues, diagonalization, and more.
• Demonstrates and explains algorithm steps for functions.
• Incorporates interactive geometric references when necessary.
• Provides tutorials on Linear Algebra concepts with clear explanations and proofs.

The application strives to maintain a user-friendly interface and uphold factual accuracy. Notably, it is advertisement-free and available at no cost. Continuous updates introduce new functions, graphs, and proofs to enhance user experience. Feedback, suggestions, and corrections are encouraged via email 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 using row reduction and recursive methods.
6. Eigenvectors and eigenvalues for real and complex matrices.
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 using Gram-Schmidt, Givens rotations, and Householder reflections methods.
14. Singular Value Decomposition with application in image compression.
15. Polar factorization.
16. Interactive graphs for transformation by 2x2 and 3x3 matrices; derivation of specific matrix types like rotation or reflection.
17. Raising a Matrix to power n (n 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).

User Interface Features:

• Retains the most recent matrix entry for a specific operation and size between program sessions.
• All input or output matrices can be saved to the clipboard for use in other applications within the app, text documents, or spreadsheets.
• Saves matrix and linear equations entries in a table format so they are accessible after reopening the application.
• Facilitates filling matrix entries with random numbers through various range options provided.
• Offers solutions as fractions for many functions; eigenvalues and eigenvectors are displayed in fractions and radicals for 2x2 matrices.
• Possibility to save tutorial items into the "My Tutorial Chapters" list along with adding comments that can be saved into the "My Comments" list for most tutorial chapters.