MuStripKit vs Matrix Solver Step by Step

MuStripKit is a versatile microstrip toolkit app for microstrip circuit analysis and design. The app realizes various functions, including microstrip line analysis and synthesis, calculations of input impedance, reflection coefficient, and frequency response in terms of S-parameters. A Smith chart tool is also provided to aid in designing a microstrip circuit. In addition, using a novel multiple 1-D FDTD method, the app shows time-domain simulation of microstrip circuits incorporated with lumped elements, including resistors, capacitors, and inductors in parallel, as well as series connections. Several educational circuit examples are provided to help illustrate the electromagnetic wave propagation in the microstrip circuit. For more information, please refer to "A Microstrip Circuit Tool Kit App with FDTD Analysis Including Lumped Elements," IEEE Microwave Magazine, vol. 16, no. 1, pp. 74-80, 2015. User interface: - touch on number field to input/change value - slider may be used to change value - swipe left/right to select circuit element - press 'Add'/'Del' to add/delete circuit element in schematic - tap to select circuit element in schematic - long press to move circuit element in schematic

“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.