Notes
- Can drop one homework
- Can drop one quiz
- https://www.mathmatize.com/c/1451/
Declaring Absence/Regrade
Mathematize
https://www.mathmatize.com/c/1451/
OH
https://q.utoronto.ca/courses/375808/pages/ta-office-hours-schedule
- IA 3100
Concepts
Fields
- Fields
- Algebra
- Binary Operations
- Additive Identity
- Multiplicative Identity
- Additive Inverse
- Multiplicative Inverse
- Commutative
- Associative
- Distributive
Vectors
- Vectors
- Tuple
- Matrix
- Linear System
- Augmented Matrix
- Echelon Form
- Elimination Algorithm
- Column Vector
- Normal Vector
- Affine Subset
- Coordinate Vector
- Matrix Vector Multiplication
Subspaces
- Subset
- Fields
- Vector Space
- Closed
- Subspace
- Redundant Vector
- Linear Independent
- Basis
- Standard Basis
- Linear Equation
- Invariance Theorem
Complex Numbers
- Complex Number
- Complex to Real Mapping
- Euler’s Imaginary Formula
- Polar Form
- Complex Number Unit Vector
- N-th Roots of Unity
- N-th Roots
Transformations
Dimensions and Basis
- Subspace Dimension
- Basis
- The Dimension Bound Theorem
- Dimension Theorem
- Surjective
- Injective
- Image and Surjectivity Theorem
- Kernels and Injectivity Theorem
- Dimension and Injectivity Theorem
- Dimension and Surjectivity Theorem
- Image and Spans Theorem
Inverses
- Linear Map Inverse
- Injective Surjective Invertable
- Automorphism
- Endomorphism
- Isomorphism
- Gauss Jordan Algorithm for Finding Inverses
Determinants
Change of Basis & Eigenvectors
- Change of Basis
- Changing Coordinates and Linear Maps
- Changing Coordinates of Endomorphic Maps
- Matrix With Base Inverse
- Eigenvector
- N-Fold Composition
- Diagonal Matrices
- Eigenvalues are Vectors in Kernels
- Characteristic Polynomial
- Finding Eigenvectors
- Finding Diagonals from Eigenvalue
- Diagonalizable
- Geometric Multiplicity
- Algebraic Multiplicity
- Geometry ⇐ Algebra Theorem