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Applied Linear Algebra _ Course Introduction
2
Vector Spaces: Introduction
3
Linear Combinations and Span
4
Subspaces, Linear Dependence and Independence
5
Basis and Dimension
6
Sums, Direct Sums and Gaussian Elimination
7
Linear Maps and Matrices
8
Null space, Range, Fundamental theorem of linear maps
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Column space, null space and rank of a matrix
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Algebraic operations on linear maps
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Invertible maps, Isomorphism, Operators
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Solving Linear Equations
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Elementary Row Operations
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Translates of a subspace, Quotient Spaces
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Row space and rank of a matrix
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Determinants
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Coordinates and linear maps under a change of basis
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Simplifying matrices of linear maps by choice of basis
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Polynomials and Roots
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Invariant subspaces, Eigenvalues, Eigenvectors
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More on Eigenvalues, Eigenvectors, Diagonalization
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Eigenvalues, Eigenvectors and Upper Triangularization
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Properties of Eigenvalues
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Linear state space equations and system stability
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Discrete-time Linear Systems and Discrete Fourier Transforms
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Sequences and counting paths in graphs
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PageRank Algorithm
28
Dot product and length in Cn, Inner product and norm in V over F
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Orthonormal basis and Gram-Schmidt orthogonalisation
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Linear Functionals, Orthogonal Complements
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Orthogonal Projection
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Projection and distance from a subspace
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Linear equations, Least squares solutions and Linear regression
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Minimum Mean Squared Error Estimation
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Adjoint of a linear map
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Properties of Adjoint of a Linear Map
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Adjoint of an Operator and Operator-Adjoint Product
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Self-adjoint Operator
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Normal Operators
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Complex Spectral Theorem
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Real Spectral Theorem
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Positive Operators
43
Quadratic Forms, Matrix Norms and Optimization
44
Isometries
45
Classification of Operators
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Singular Values and Vectors of a Linear Map
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Singular Value Decomposition
48
Polar decomposition and some applications of SVD
Description:
PRE-REQUISITES: Basic Calculus, Should have done a basic (or a first) course in Linear Algebra INTENDED AUDIENCE: Senior level Undergraduate and First year Postgraduate/PhD INDUSTRIES APPLICABLE TO: Communications, Artificial Intelligence, Analytics COURSE OUTLINE: Introduce the fundamentals of vector spaces, inner products, linear transformations, and eigenspaces to electrical engineering students. And teach Applied Linear Algebra, Vector Spaces: Introduction. Linear Combinations and Span. Subspaces, Linear Dependence and Independence. Basis and Dimension. Sums, Direct Sums and Gaussian Elimination. Linear Maps and Matrices.

Applied Linear Algebra

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#Mathematics #Algebra #Linear Algebra #Vector Spaces #Determinants #Eigenvalues #Eigenvectors #Orthogonal Projections #Singular Value Decomposition
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Applied Linear Algebra _ Course Introduction