Member-only story
Bird’s-Eye View of Linear Algebra: Left, Right Inverse => Injective, Surjective Maps
If matrix multiplication isn’t commutative, then why don’t we have left and right inverses?
Note: all images unless otherwise specified are by the author.
This is the seventh chapter of the in-progress book on linear algebra: “A birds eye view of linear algebra”. The table of contents so far:
- Chapter-1: The basics
- Chapter-2: The measure of a map — determinants
- Chapter-3: Why is matrix multiplication the way it is?
- Chapter-4: Matrix chain multiplication
- Chapter-5: Systems of equations, linear regression and neural networks
- Chapter-6: Rank nullity and why row rank == col rank
- Chapter-7: Left-right inverse => injective-surjective maps
- Chapter-8 (current): Orthonormal matrices
We covered matrix multiplication in some depth in chapter 3. We mentioned that there is an identity element for matrix multiplication, which is the matrix: