Change of Base in Linear Applications

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Introduces the concept of basis and canonical basis in linear algebra, essential for vector space representation.

Explains orthogonal matrices, Gram-Schmidt process, and best vector approximation in subspaces.

Explores matrix equivalence, consistency, row generation, and reduced row echelon form implications.

Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

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

Introduces Eigen and Pybind libraries for linear algebra operations and C++ function binding to Python.

Covers linear independence, bases, change of basis, and vector representation.

Covers echelon matrices, vector equations, linear combinations, and vector spans in R^n.

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