From the course: Machine Learning Foundations: Linear Algebra
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Gaussian elimination and finding the inverse matrix
From the course: Machine Learning Foundations: Linear Algebra
Gaussian elimination and finding the inverse matrix
- [Instructor] Linear equations can be solved in a few different ways. Two of the most applied techniques are elimination method and substitution method. However, in linear algebra, we have a different technique using matrix inversion. It is a convenient method for solving a system of linear equations. In mathematics, the concept of inversion is well known starting from real numbers. A real number a is set to have an inverse if there exist a number b such that a multiply with b equals 1. Any nonzero number a has an inverse b. The nice thing is that we can generalize the concept on inverses to matrices. Inverse of matrix A is denoted as A to the power of minus 1, where minus 1 is a super script. If we multiply inverse of the matrix with the original matrix, we get, as a result, identity matrix. By definition, a matrix B such that A multiplied with B equals B multiplied with 1 equals I is called an inverse of the…
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