Mathematical Immaturity

2. Linear Transformations and Matrices

2.1. $\quad$Linear transformations
2.2. $\quad$Null space and range
2.3. $\quad$Nullity and rank
2.4. $\quad$Exercises
2.5. $\quad$Algebraic operations on linear transformations
2.6. $\quad$Inverses
2.7. $\quad$One-to-one linear transformations
2.8. $\quad$Exercises
2.9. $\quad$Linear transformations with prescribed values
2.10. $\quad$Matrix representations of linear transformations
2.11. $\quad$Construction of a matrix representation in diagonal form
2.12. $\quad$Exercises
2.13. $\quad$Linear spaces of matrices
2.14. $\quad$Isomorphism between linear transformations and matrices
2.15. $\quad$Multiplication of matrices
2.16. $\quad$Exercises
2.17. $\quad$Systems of linear equations
2.18. $\quad$Computation techniques
2.19. $\quad$Inverses of square matrices
2.20. $\quad$Exercises
2.21. $\quad$Miscellaneous review exercises on matrices