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Lecture
Change of Variables Theorem
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Linear Algebra: Multilinear Groin and Determinants
Explores multilinear groin and determinants, including the Sarrus rule and proof by induction.
Change of Variables Theorem
Explores the change of variables formula in higher dimensions and its application through an example.
Linear Independence: The Wronskian Concept
Explains the Wronskian and its role in determining linear independence of solutions to differential equations.
Projected Gradient Descent
Explores Projected Gradient Descent and related optimization methods using Bregman Divergence.
Matrix Calculus: Determinants
Covers the calculation of determinants in matrix algebra and their application in solving linear equations.
Determinants: Alternate Forms and Symmetrization
Explores alternate forms, symmetric forms, and determinants in linear algebra.
Linear Algebra: Equivalence and Calculations
Explains equivalence in linear algebra and set calculations with illustrative examples.
Linear Independence: The Wronskian Concept
Explains the Wronskian and its role in determining linear independence of solutions to differential equations.
Theorems in Analysis
Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.
Geometric Transformations in R2 and R3
Explores geometric transformations in R2 and R3, including linear transformations, projections, matrices, and trace properties.