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invertible matrix

a square matrix that possesses an inverse

Inverse

a + (-a) = 0 = (-a) + a OR a * 1/a = 1 = 1/a * a; a cant be 0

singular matrix

a matrix that has no inverse

nonsingular matrix

an invertible matrix

elementary matrix

an invertible matrix that results by performing one elementary row operation on an identity matrix

determinant

ad-bc; must be nonzero for an invertible matrix

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

Conditions for inverse

in an mxn Matrix A

Inverse => L.I. ?

every column is L.I. - all pivot column