Last updated April 10, 2022

Status: Tags: Links: ) MATH 232 - Applied Linear Algebra

Math 232 Course Outline

• MATH 232 Vocabulary
• MATH 232 Dimensions

Vectors

• Euclidean n-Space
• Span
• Linear Independence and Dependence
• Basis
• Dot Product and Orthogonality
• Lines and Planes

Systems of Linear Equations

• Row Reduction (Gaussian elimination) to Echelon form
• The Geometry of Linear Systems
• Applications in business, science and engineering

Matrices

• Matrix operations
• Matrix inverse; and properties of matrices
• Elementary matrices and calculating matrix inverses
• Matrices with special forms.

Linear Transformations

• Matrices as transformations
• Geometry of Linear Transformations
• Kernel and range
• Composition and Invertibility
• Application to Computer Graphics (optional)

Determinants

• Calculating determinants
• Properties of determinants
• Cramer’s rule (optional)

Complex Numbers

• Arithmetic in Cartesian co-ordinates.
• The complex plane, complex conjugate, magnitude and argument (phase).
• Polar form, De Moivre’s formula and Euler’s formula.
• Roots of quadratic polynomials.

Eigenvalues and Eigenvectors

• Properties and geometry
• Complex eigenvalues and complex eigenvectors
• Dynamical Systems and Markov Chains
• Application to Economics: the Leontief model (optional)
• The Power Method; Application to Internet Search Engines
• Matrix Similarity and Diagonalization

Subspaces of R^n

• Subspaces and Linear Independence
• Basis and Dimension
• The Fundamental Spaces of a Matrix
• Rank
• Change of basis

Orthogonality

• Projection
• Orthogonal bases and the Gram Schmidt process
• Orthogonal matrices (optional)
• Application to least squares approximation

Backlinks

1

list from Math 232 Course Outline AND !outgoing(Math 232 Course Outline)

References:

Created:: 2022-01-10 13:02