Linear Algebra › Section B · Matrix algebra › Topic B.3
The invertible matrix theorem
Pivots, independence, spanning, one-to-one maps and inverses looked like separate ideas. For a square matrix they are one idea seen from many sides: either every statement on a long list is true, or every one is false.
In this topic
- Many questions, one answer
- The theorem
- Why square matters
- One-sided inverses are enough
- Using the theorem both ways
- Worked example: a singular 3 × 3
- Worked example: reasoning without numbers
- Invertible linear transformations
- Nearly singular matrices
- Common mistakes to avoid
- Key takeaways
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