Math 115

#class

Linear Algebra for Engineering

Prereqs: MCV4UI

Vaecter
- Prof. Michelle Molino

Apples are Vaecters
- Prof. Michelle Molino

1. Complex Numbers
   • Complex Numbers in Standard Form
   • Conjugate and Modulus
   • Polar Form
   • Powers and Roots of Complex Numbers
   • Complex Polynomials
2. Vectors
   • The Vector
   • Norms and Dot Products
   • Complex Vectors
   • Cross Product
   • Vector Equation of a Line
   • Vector Equation of a Plane, Scalar Equation of a plane
   • Projections, Distances From Points to Lines and Planes
3. Systems of Linear Equations
   • Systems of Linear Equations
   • Rank
   • Homogeneous Systems of Linear Equations
   • Applications
     • Balancing Chemical Reactions
     • Linear Models
     • Network Flow
     • Electrical Networks
4. Matrix Algebra
   • Matrices and Basic Operations
   • The Matrix-Vector Product
   • Matrix Multiplication
   • Applications
     • Adjacency Matrices for Directed Graphs
     • Markov Chains
   • Complex Matrices
   • Matrix Inverses
5. Vector Spaces
   • Spanning Sets
   • Linear Dependence and Independence
   • Subspaces of Real Vectors
   • Bases of Subspaces
   • Dimension of a Subspace
   • Three Fundamental Subspaces Associated With a Matrix
   • Vector Spaces
   • Polynomials As Vectors
   • Vector Spaces Over Complex Numbers
6. Linear Transformations
   • Matrix Transformations and Linear Transformations
   • Geometric Transformations
   • Operations on Linear Transformations
   • Kernel and Range of a Linear Transformation
7. Determinants
   • Determinants, Adjugates, Matrix Inverses, and Elementary Row/Column Operations
   • Properties of Determinants
   • Application: Polynomial Interpolation
8. Eigenvalues and Eigenvectors, Diagonalization
   • Eigenvalues and Eigenvectors, Characteristic Polynomials
   • Diagonalization
   • Power of Matrix, Trace
   • Orthogonal Sets and Bases
   • Orthogonal Matrices
   • Gram-Schmidt Procedure
   • Orthogonal Diagonalization