Applied Linear Algebra

Applied Linear Algebra

@VTU COE

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What you will learn

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Introduce the fundamentals of vector spaces, inner products, linear transformations, and eigenspaces to electrical engineering students.

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Linear Maps and Matrices
Preview 38:44
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Null space, Range, Fundamental theorem of linear maps
Preview 38:51
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Column space, null space and rank of a matrix
Preview 25:09
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Algebraic operations on linear maps
Preview 22:24

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Invertible maps, Isomorphism, Operators
Preview 32:01
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Solving Linear Equations
Preview 25:29
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Elementary Row Operations
Preview 34:55
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Translates of a subspace, Quotient Spaces
Preview 29:13

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Row space and rank of a matrix
Preview 40:49
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Determinants
Preview 40:13
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Coordinates and linear maps under a change of basis
Preview 29:41
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Simplifying matrices of linear maps by choice of basis
Preview 17:57

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Polynomials and Roots
Preview 35:35
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Invariant subspaces, Eigenvalues, Eigenvectors
Preview 34:04
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More on Eigenvalues, Eigenvectors, Diagonalization
Preview 40:54
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Eigenvalues, Eigenvectors and Upper Triangularization
Preview 34:15

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Properties of Eigenvalues
Preview 12:05
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Linear state space equations and system stability
Preview 26:14
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Discrete-time Linear Systems and Discrete Fourier Transforms
Preview 23:17
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Sequences and counting paths in graphs
Preview 17:12
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PageRank Algorithm
Preview 17:49

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Dot product and length in Cn, Inner product and norm in V over F
Preview 49:36
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Orthonormal basis and Gram-Schmidt orthogonalisation
Preview 25:01
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Linear Functionals, Orthogonal Complements
Preview 41:13

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Orthogonal Projection
Preview 27:38
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Projection and distance from a subspace
Preview 30:39
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Linear equations, Least squares solutions and Linear regression
Preview 26:22
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Minimum Mean Squared Error Estimation
Preview 16:42

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Adjoint of a linear map
Preview 20:15
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Properties of Adjoint of a Linear Map
Preview 45:41
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Adjoint of an Operator and Operator-Adjoint Product
Preview 32:05

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Self-adjoint Operator
Preview 30:42
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Normal Operators
Preview 24:43
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Complex Spectral Theorem
Preview 31:43
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Real Spectral Theorem
Preview 22:08

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Positive Operators
Preview 34:26
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Quadratic Forms, Matrix Norms and Optimization
Preview 38:12
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Isometries
Preview 30:47
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Classification of Operators
Preview 15:29

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Singular Values and Vectors of a Linear Map
Preview 31:06
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Singular Value Decomposition
Preview 36:46
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Polar decomposition and some applications of SVD
Preview 35:28
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Meet Your Instructor
@VTU COE
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Instructor
3.3 Rating
8558 Students
802 Courses
About Instructor

VTU is one of the largest Technological Universities in India with 24 years of Tradition of excellence in Engineering & Technical Education, Research and Innovations. It came into existence in the year 1998 to cater the needs of Indian industries for trained technical manpower with practical experience and sound theoretical knowledge.

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Free

  • Course Duration
    23 h 48 m 53 s
  • Course Level
    Intermediate
  • Student Enrolled
    0
  • Language
    English
This Course Includes
  • 23 h 48 m 53 s Video Lectures
  • 2 Quizzes
  • 0 Assignments
  • 0 Downloadable Resources
  • Full Lifetime Access
  • Certificate of Completion