| Term | Definition |
|---|
| determinant | ad-bc; must be nonzero for an invertible matrix |
| elementary matrix | a matrix that is obtained by performing a single elementary row operation on an identity matrix; invertible (the inverse of E is the elementary matrix of the same type that transforms E back into I) |
| algorithm for finding inverse | row reduce the augmented matrix [A I]. If A is row equivalent to I, then [A I] is row equivalent to [I A^-1] (otherwise, A doesn't have an inverse) |
| AB = I | If _______, A and B are both invertible and inverses of each other |
| invertible linear transformation T | there exists a function S: R^n -> R^n such that S (T(x)) = x for all x in R^n and T(S(x))=x for all x in R^n |
| inverse of transformation T | S such that T is invertible |
Combine with other sets
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