Lectures related to Linear constraints: Basic directions

Orthogonality and Gram-Schmidt Process

Explores orthogonality, Gram-Schmidt process, dot products, and solution minimization in systems.

Optimal Decision Making: Sensitivity Analysis

Covers sensitivity analysis in linear programming, focusing on optimal solutions and their sensitivities to changes.

Vector Products: Dot and Cross - Part 2

Covers the concepts of dot and cross products of vectors and their applications.

Fourier Analysis: Stokes Theorem

Explores the application of Stokes' theorem to surfaces and vector spaces in Fourier analysis.

Indicial Notation and Tensor Components

Covers the manipulation of indicial notation and tensor components, focusing on concepts such as indical notation, free indices, contraction, and the dot product.

Vector Components and Operations

Covers vector components, projections, conventions, operations, and mathematical identities.

Surface Integral: Understanding Variable Positions

Explores surface integrals and variable positions, emphasizing sign inversion and induced paths.

Linear Programming: Weighted Bipartite Matching

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.

Geometric Properties of Dot Product

Covers the geometric properties of the dot product and its algebraic aspects.

Derivatives and Differential Equations

Covers trigonometric functions, derivatives, differential equations, and vector properties.

Support Vector Machine: Primal Formulation with Hard Margin

Covers the Support Vector Machine with a hard margin formulation and the importance of maximizing the margin between classes.

Metric Tensor: Definition

Explores the definition and properties of the metric tensor, enabling control of geometric quantities and lengths.

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Gradient Descent: Optimization and Constraints

Discusses gradient descent for optimization with equality constraints and iterative convergence criteria.

Vectors: Dot Product

Covers the dot product between vectors and orthogonal projections.

Summary using nabla symbol

Covers the concept of nabla symbol, vector scalar, divergence, and cross product in 3D.

Dot Product: Properties and Applications

Explores the properties and applications of the dot product in vector spaces.

Tensor Operations: Dot and Cross Products

Covers tensor operations, focusing on dot and cross products and their geometric interpretation.

Dot Product: Definition and Geometric Interpretation

Explains the dot product of vectors and its geometric interpretation as signed volume.

Physics 1: Vectors and Dot Product

Covers the properties of vectors, including commutativity, distributivity, and linearity.