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Natural Cubic Splines
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Linear Algebra: Matrices and Linear Applications
Covers matrices, linear applications, vector spaces, and bijective functions.
Matrix Operations and Vector Spaces
Covers elementary matrix operations and vector spaces, including properties and conditions for invertibility.
Matrix Representations: Linear Maps
Explores matrix representations of linear maps and their invariance, using examples and special cases.
Linear Transformations and Basis Changes
Covers the concept of interesting subspaces related to matrices and the change of basis matrix.
Singular Value Decomposition: Applications and Interpretation
Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.
Linear Transformations: Kernel and Image
Covers the concepts of kernel and image of a linear transformation and their relationship with the rank of the matrix.
Linear Transformations: Matrices and Bases
Covers the determination of matrices associated with linear transformations and explores the kernel and image concepts.
Vector Spaces: Properties and Operations
Covers the properties and operations of vector spaces, including addition and scalar multiplication.
Linear Algebra: Matrix Representation
Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.
Matrix Operations: Rank and Inclusion in Vector Spaces
Explores matrix rank and vector space inclusion through elementary row operations.