Linear Algebra vs Linear Algebra World

Linear Algebra - Matrix Solver is a powerful and easy-to-use tool for calculating matrices, determinants, and vector operations — perfect for students, engineers, and anyone who works with linear algebra in study or professional tasks. The app performs step-by-step calculations with detailed solutions using the correct formulas. You can work with matrices up to 5×5 and vectors in 2D or 3D. Each calculator includes a brief theoretical overview to help you understand the concept behind the operation. It also includes a random number generator to instantly create practice problems with random values. Available in 8 languages: English, French, German, Italian, Portuguese, Spanish, Russian, Ukrainian. Whether you're learning, teaching, or solving real-world problems, Linear Algebra app helps you get accurate results quickly and understand the math behind them. The application perform following operations with matrices: • Matrix addition • Matrix subtraction • Matrix scalar multiplication • Matrix square • Matrix multiplication • Matrix transposition Determinant calculations: • Calculation of the determinant using the Sarrus method • Calculation of the determinant using the Laplace method Vector operations: • Vector Length • Vector coordinates by two points • Vectors addition • Vectors subtraction • Scalar and vector multiplication • Scalar product of vectors • Cross product of vectors • Mixed (scalar) triple product • Angle between two vectors • Projection of a vector onto another vector • Direction cosines • Collinear vectors • Orthogonal vectors • Coplanar vectors • Area of triangle formed by vectors • Area of a parallelogram formed by vectors • Volume of pyramid formed by vectors • Volume of a parallelepiped formed by vectors Download now and simplify your linear algebra work!

Linear Algebra World (LAW) presents linear algebra in a way that is accessible yet rigorous. It is designed for students of engineering, mathematics, data science and related fields, and may also serve as a visual presentation tool for instructors. The app combines three roles: • matrix calculator • interactive algorithm step visualizer • carefully designed learning pathway through linear algebra Our goal is to present linear algebra as a coherent system built on a small set of axioms. Definitions are separated from consequences, logical dependencies are made explicit, and notation is kept minimal to reduce cognitive load. Visual tools are used extensively—even for abstract topics such as the four fundamental subspaces—so that geometric intuition and algebraic reasoning reinforce one another. The curriculum begins with vectors as coordinates and matrices as collections of vectors, and currently covers topics through QR factorization. Upcoming additions include OLS, eigendecomposition, SVD, and PCA. This app builds on our earlier Matrix Solver Step by Step, a highly rated matrix computation app used by students for several years. LAW adds a structured curriculum along with LaTeX import and export. LAW is designed for serious learners who want to understand the structure behind the computations. For quick step-by-step matrix calculations, Matrix Solver Step by Step may be the more direct tool. Your constructive feedback is essential to the continued refinement of the app.