# MATB24

On this page is optional material for tutorials and tutorial notes (submitted after the next tutorial occurs) for enhancing your study in MATB24.

# Extra material

- Alternative method for finding a Jordan canonical form of a matrix
- Past 2015 final: Some sample solutions

# Tutorial material

Reference sheets are definitions and theorems relevant to the tutorial. These are optional to bring to tutorial (printed, on device).

- Question: Can you replace a basis vector with a linear combination of others?
- Question: Different method to find basis for spanning set?
- Question: How does nullity and rank relate to being one-to-one and onto?
- Question: What does it mean for the determinant to be multilinear and alternating?
- Week 4 tutorial reference sheet
- Week 5 tutorial reference sheet
- Week 6 tutorial reference sheet
- Week 7 supplementary examples (inner products)
- Week 7 tutorial reference sheet
- Week 8 tutorial reference sheet
- Week 9 tutorial reference sheet
- Week 10 supplementary examples (eigenvalues/vectors, diagonalization)
- Week 10 tutorial reference sheet
- (No reference sheet for Week 10)
- Week 12 tutorial reference sheet

# Tutorial notes

- Week 2 tutorial notes (vector spaces and fields)
- Week 3 tutorial notes (spanning sets and coordinate vectors)
- Week 4 tutorial notes (finding bases)
- Week 5 tutorial notes (ordered bases, linear transformations)
- Week 6 tutorial notes (Quiz 2, midterm review)
- Week 7 tutorial notes (rank equation, inner products)
- Week 8 tutorial notes (computing determinants)
- (No notes for Week 9)
- Week 10 tutorial notes (eigenvalues/vectors, complex algebra)
- Week 11 tutorial notes (diagonalizability, complex matrices, inner product spaces)
- Week 12 tutorial notes (change-of-coordinates matrix, diagonalizability, orthogonal, similar matrices)

# Lecture notes

These are my notes when I substituted those three lectures.

- July 14 lecture notes (Gram-Schmidt process)
- July 18 lecture notes (change-of-coordinates matrix, diagonalizability)
- July 21 lecture notes (diagonalization, spectral theorems)

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