Metrics: Line and Convex Cone

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Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Explores convex functions, global minima, and their relationship with differentiability.

Explores linear independence in vector spaces and the concept of bases.

On Convex Optimization covers course organization, mathematical optimization problems, solution concepts, and optimization methods.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Introduces linear combinations of vectors in R^n and their properties.

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Explores forming bases, dependencies, and relationships in linear applications using invertible matrices and canonical bases.