Intro to Linear Algebra

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Exams

Assignments

The majority of the assignments in 2013 were online via WeBWork, and Assignments 1 and 2 for Winter 2018 were identical to those in Winter 2015.

Notes

These notes, with a couple of exceptions including the first day, are from my iPad using GoodNotes.

  • Day 1 -Motivation and Applications
  • Day 2 -Systems of Linear Equations; m-vectors; Matrices
  • Day 3 -Using Matrices to Solve Systems of Linear Equations
  • Day 4 -Application: Balancing Chemical Equations; R^n; First Proof in the Class
  • Day 5 -Row-Reduced Echelon Form; Homogeneous Linear Equations; Span and Linear Combinations of Vectors
  • Day 6 -Inhomogeneous Linear Equations; More on Span; Linear Independence
  • Day 7 -Dot Product; Norms on R^n; Angles Between Vectors
  • Day 8 -Proving the 2-Norm is a Norm; Extending Linear Independence; Orthogonality
  • Day 9 -Orthogonality and Linear Independence; Transpose of a Matrix; Application: Electrical Circuits
  • Day 10 -Application Continued: Electrical Circuits, Ohm's Law and Kirchoff's Current Law
  • Day 11 -Matrix Operations; Linearity
  • Day 12 -Properties of Matrix Operations; Zero and Identity Matrix; Invertibility of Square Matrices
  • Day 13 -Permutations; Definition of Determinant; Invertibility and the Determinant
  • Day 14 -Finding Inverses; Solving Linear Equations via Inverses; Properties of Transpose, Inverse, and Determinant
  • Day 15 -Examples of Determinant Properties; Upper and Lower Triangular Matrices; Diagonal Matrices
  • Day 16 -Proofs of Determinant Properties; Application: Computer Graphics
  • Day 17 -Application Continued: Computer Graphics, Homogeneous Coordinates; Real Vector Spaces: Definition and Examples
  • Day 18 -Subspaces: Definition and Examples; Subspace Test
  • Day 19 -Basis and Dimension of a Real Vector Space; Subordination of Dimension for Subspaces
  • Day 20 -Elementary Matrices: a Basis for M_n(R); The Matrix of a Linear Transformation Between Finite-Dimensional Real Vector Spaces
  • Day 21 -Change of Basis Formula; Isomorphisms
  • Day 22 -Subspaces Associated to a Matrix: Range, Nullspace, Rowspace, and Column Space; Rank-Nullity Theorem
  • Day 23 -Application: Signal Processing, Casorati Matrix, Linear Difference Equations
  • Day 24 -Eigenvalues and Eigenvectors: Definitions and Examples; How to Find Eigenvalues for a Matrix
  • Day 25 -Characteristic Polynomial; Similarity and Eigenvalues; Powers of a Diagonalizable Matrix
  • Day 26 -More on Diagonalizability; Eigenvalues for Orthogonal and Positive Semi-Definite Matrices; Orthogonal Diagonalizability of Symmetric Matrices
  • Day 27 -Application: Google's PageRank, Perron-Frobenius Theorem
  • Day 28 -Properties of Eigenvalues; Matrix Norm; Square Roots, Absolute Values, and Polar Decomposition
  • Day 29 -Orthogonal Projections: Definition and Examples, Diagonalization
  • Day 30 -Form of Orthogonal Projections; Application: Least Squares
  • Day 31 -Application Continued: Least Squares, Best-Fit Lines and Quadratics
  • Day 32 -The Gram-Schmidt Process
  • Special Day -Singular Value Decomposition and Principal Component Analysis
  • Special Day -Image Compression

    • Notes By Topic

    These notes are from my iPad using Noteshelf. They are not tied to a particular day but are instead arranged by content and are more current than the above. I think my handwriting looks great, but your standards may be higher.

  • Interpolating Polynomials
  • Vectors
  • Matrices
  • Matrix-Vector Multiplication
  • Matrix Operations
  • Invertibility
  • Computer Graphics
  • Determinants
  • Introduction To Mathematical Proofs
  • Vector Spaces
  • Linear Transformations
  • Best-Fit Polynomials
  • Projections
  • Orthonormal Bases
  • Eigenvalues and Eigenvectors
  • PageRank
  • Diagonalization
  • Singular Vaue Decomposition
  • Principal Component Analysis

    • Resources

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