From the course: Machine Learning Foundations: Linear Algebra
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Inverse and determinant
From the course: Machine Learning Foundations: Linear Algebra
Inverse and determinant
- [Instructor] The determinant of a matrix is a scalar that has a few important characteristics. It enables us to map a square matrix to a scalar and allows us to determine if a matrix can be inverted. We can denote a determinant for a matrix A as detA. There are two important properties for a determinate. In the case when determinate A equals zero, this means the inverse matrix cannot be computed, since the inverse matrix of matrix A would be calculated as 1 divided by detA, meaning we would have to divide 1 by 0. And we cannot divide 1 by 0. In this special case, matrix A is singular, meaning it contains only linearly-dependent columns. To calculate a determinant for a two-by-two matrix, we have to memorize a simple formula. If our matrix A has elements a, b, c, and d, then formula to calculate a determinant for matrix A is determinant of A equals a multiplied with d minus b multiplied with c. Let's explore a simple…
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