Matrix Inverse
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Given a matrix M, the inverse matrix is a new matrix M-1 that when multiplied by M, gives the identity matrix.
Matrix inverse is a high school-level concept that would be first encountered in a linear algebra course. It is listed in the California State Standards for Linear Algebra.
Prerequisites
| Inverse Function: | The inverse function f-1 of a function f is the function for which f(f-1(x)) = x for any x. |
| Linear Transformation: | A function from one vector space to another. If bases are chosen for the vector spaces, a linear transformation can be given by a matrix. |
| Matrix: | A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, for every linear transformation, there exists exactly one corresponding matrix, and every matrix corresponds to a unique linear transformation. The matrix is an extremely important concept in linear algebra. |
| Matrix Multiplication: | Matrix multiplication is the process of multiplying two matrices (each of which represents a linear transformation), which forms a new matrix corresponding to the matrix representation of the two transformations' composition. |