14.3 The Invertible Matrix Theorem Part 3

#Type/Theorem #Topic/Linear_Algebra

Types: 14.1 The Invertible Matrix Theorem Part 1, 14.2 The Invertible Matrix Theorem Part 2
Examples: N/A
Constructions: N/A
Generalizations: N/A

Properties: N/A
Sufficiencies: N/A
Questions: N/A

The Invertible Matrix Theorem: Part 3

Let $A \in R^{n \times n}$ be a square matrix with real entries. Then, the following statements are equivalent $⟺$ . In other words, for a given matrix $A$ , the statements are either all true or false.
23. The number 0 is not an eigenvalue of $A$ .
24. The matrix $A$ has $n$ non-zero singular values.