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Properties of Full Rank Matrices 📂Matrix Algebra

Properties of Full Rank Matrices

Theorem1

Let’s refer to $A$ as matrix $m \times n$. Then, the necessary and sufficient condition for $A$ to have a full rank is for $A^{T}A$ to be an invertible matrix.

Proof


  1. Howard Anton, Elementary Linear Algebra: Aplications Version (12th Edition, 2019), p422 ↩︎