| |  | | MA 261 MA 261 -- Linear Algebra
- Systems of Linear Equations
a) Introduction
b) Gaussian Elimination and Gauss-Jordan Elimination
- Matrices
a) Operations and properties
b) Inverse of a matrix
c) Elementary matrices
- Determinants
a) The determinant of a matrix
b) Evaluation of a determinant using elementary operations
c) Properties
- Vector Spaces
a) Vectors in Rn
b) Vector spaces
c) Subspaces of vector spaces
d) Spanning sets and linear independence
e) Basis and dimension
f) Rank of a matrix and systems of linear equations
g) Change of basis
- Inner Product Spaces
a) Length and dot product in Rn
b) Inner product spaces
c) Orthonormal bases: Gram-Schmidt Process
d) Mathematical models and Least Square Analysis
- Linear Transformations
a) Introduction
b) Kernel and range of a linear transformation
c) Matrices for linear transformations
d) Transition matrices and similarity
- Eigenvalues and Eigenvectors
a) Introduction
b) Diagonalization
c) Symmetric matrices and orthogonal diagonalization
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