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Lecture
Orthogonality and Subspace Relations
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Linear Algebra: Abstract Concepts
Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.
Orthogonality and Least Squares Method
Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.
Norms and Orthogonality
Explores norms, orthogonality, and the Pythagorean theorem in vector spaces.
Polynomials: Operations and Properties
Explores polynomial operations, properties, and subspaces in vector spaces.
Vector Spaces: Structure and Bases
Covers vector spaces, bases, and decomposition of vectors in R³.
Linear Independence and Bases
Covers linear independence, bases, and coordinate systems with examples and theorems.
Signal Representations
Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.
Linear Transformations: Kernels and Images
Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.
Linear Transformations: Matrices and Bases
Covers the determination of matrices associated with linear transformations and explores the kernel and image concepts.
Linear Applications: Definitions and Properties
Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.