ThmDex – An index of mathematical definitions, results, and conjectures.

Real square matrix invertible iff transpose is

Formulation 0

Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that

(i)	$A^T$ is a D5841: Real matrix transpose for $A$

Then the following statements are equivalent

(1)	$A$ is an D5871: Invertible real matrix
(2)	$A^T$ is an D5871: Invertible real matrix

Proofs

Proof 0

Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that

(i)	$A^T$ is a D5841: Real matrix transpose for $A$