Touch Matrix Algebra

Learning linear algebra? Need to see step by step how to bring a matrix to (reduced) row echelon form by Gaussian elimination? Or better yet, want to carry out the elementary row operations yourself? ... without getting bogged down in arithmetic, and learn one of the most important algorithms in mathematics, physics and computer science?

***If you need advanced numerical linear algebra features like eigensystem determination or singular value decomposition, be sure to check out Touch Matrix Algebra Pro.***

Introducing 'Touch Matrix Algebra', a completely unique way of working with matrices: by touch! It's almost fun. Here are some of the unique features of this mathematics app:

• drag and drop colour coded matrices to perform binary operations (e.g. matrix multiplication);
• tap to edit, long press to operate on a single matrix;
• work with either arbitrary precision matrix elements as rational numbers (rational matrices), or conventional fixed-precision, floating point numbers (decimal matrices). Convert the former into the latter;
• see the detailed, step-by-step calculation of the Gaussian algorithm that brings a matrix to row-echelon or reduced row-echelon form, and calculates a matrix inverse, rank or determinant (for rational matrices)...
• or better yet... in editing mode, highlight rows and instruct the app to carry out the elementary row operations yourself! Learn the essence of the algorithm without the hassle of carrying out the arithmetic details.
• factorize a matrix into Lower and Upper triangular matrices (up to a Permutation matrix): PLU decomposition.

Most of the basic linear algebra operations that can be done EXACTLY with rational numbers are implemented here.

The basic version of the app allows you to work with matrices up to size 3 × 3.

Unlock matrix size restrictions (and remove ads/enable offline mode) to blow the doors off, and create (essentially) arbitrarily large matrices. So you can drag race your new triple core iPad Air 2 against your friend's old iPhone 4s, and invert that random 1500 × 1500 decimal matrix . And while you're at it, do a PLU decomposition on a 1000 × 2000 decimal matrix... at the same time. (Just remember to turn off show calculations!) Touch Matrix Algebra is not only multithreaded, but the Gaussian algorithm is parallelized. It's sick: benchmark any iOS device!

Also as of V1.1: unlock 3D Graphing Support - turns Touch Matrix Algebra into a beautiful, inexpensive 3D graphing calculator, and 3D graph all of your large matrices.


Designed by an educator, mathematician and physicist.

Coded in Swift, Objective-C, and C++.

更新履歴
* Final update for legacy devices as OpenGL is deprecated in favor of Metal starting with iOS 12, and 32-bit apps/devices are no longer supported. Metal/iPhone X support coming with next version.*

Major new update...
• Touch Matrix Algebra works and plays nicely with others: Import/Export and Copy/Paste of rational or decimal matrices to and from Touch Matrix Algebra as simple comma or tab delimited text files. Tested with 'Numbers' and 'Excel', e-mail, iMessage, and Notes.
• now defunct iAd infrastructure removed (ignore IAP references to advertising)
• New linear algebra features:
- compute the null space/kernel and column space/image of a matrix (apply these ops to the transpose to get the other two fundamental subspaces)
- new general linear system solver as a binary matrix operation: simply drop matrix 'A' onto column(s) 'b' to solve Ax = b. Works with underdetermined or overdetermined linear systems in which respectively the kernel/homogeneous solution + particular/inhomogeneous solution, or the least squares approximate solution are presented. Also detects inconsistent systems for the square matrix case.
• New convenience features:
- by popular request: rename matrices (including assigning subscripts)
- re-color a matrix, or delete all matrices of a given color (i.e. derived from an originator matrix)
- delete all matrices by double-tapping an empty space
- 3D graphing (via IAP) now uses 'arc ball' coordinates for rotation instead of spherical coordinates for smoother singularity free rotation
- set the maximum value to use when generating random matrices
• Massive under the hood changes:
- the arbitrary precision engine for rational arithmetic has been re-written to use base one billion (instead of base 10) and the arithmetic (especially division) algorithms optimized; the exact (rational number) matrix algorithms now run typically 300% faster on all (64-bit) iOS hardware. (One billion is the largest power of 10 base that can be used with 64 bit integer arithmetic without overflow on multiplication.)
- updated for Swift 3.0/4.0 compatibility, while maintaining full support for older iOS devices (back to iOS 8.1 and the venerable iPad 2).