Invertible Matrix Theorem

Statements that are equivalent to a square matrix being invertible; examples.

Created On

August 21st, 2017

6 years ago

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• Equivalence theorem: the matrix A row-reduces to the identity matrix. math.la.t.equiv.identity

• The inverse of a matrix (if it exists) can be found by row reducing the matrix augmented by the identity matrix. math.la.t.mat.inv.augmented

• Equivalence theorem: the matrix A has a left inverse. math.la.t.equiv.inv.left

• Equivalence theorem: the matrix A has a right inverse. math.la.t.equiv.inv.right

• Matrix inverse is an involution. math.la.t.mat.inv.involution

• The inverse of a matrix can be used to solve a linear system. math.la.t.eqn.mat.inv

• Definition of nonsingular matrix: matrix is invertible math.la.d.mat.nonsingular.inv

• Definition of matrix inverse math.la.d.mat.inv