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Linear Algebra for AI - Period 4 Honors Program Program Spring 2025 Semester - Extended - Amsterdam

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Linear Algebra for AI - Period 4

Linear Algebra for AI - Period 4 Course Overview


CEA CAPA Partner Institution: Vrije Universiteit Amsterdam
Location: Amsterdam, Netherlands
Primary Subject Area: Mathematics
Other Subject Area: Computer Sciences
Instruction in: English
Course Code: XB_0081
Transcript Source: Partner Institution
Course Details: Level 200
Recommended Semester Credits: 3
Contact Hours: 84


The topics that will be treated are listed below. For every topic, the relevant concepts are listed.

Linear systems: linear system (consistent/inconsistent/homogeneous/inhomogeneous), augmented) coefficient matrix, row equivalence, pivot position/column, (reduced) echelon form, basic/free variable, spanning set, parametric vector form, linear (in)dependence.
Linear transformations: linear transformation, (co)domain, range and image, standard matrix, one-to-one and onto, singularity, determinant, elementary matrices.
Subspaces and bases: subspace, column and null space, basis, coordinate system, dimension, rank.
Eigenvalues and eigenvectors: eigenvalue, eigenvector, eigenspace, characteristic equation/polynomial, algebraic multiplicity, similarity, diagonalization and diagonalizability.

Orthogonality: dot product, norm, distance, orthogonality, orthogonal complement, orthogonal set/basis, orthogonal projection, orthonormality, orthonormal basis, Gramm-Schmidt process, least squares problem/solution, orthogonal diagonalization, singular value/vector, singular value decomposition, Moore-Penrose inverse.

Vrije Universiteit Amsterdam (VU Amsterdam) awards credits based on the ECTS system. Contact hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.

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