Professor: César J. Niche
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Schedule and classroom
Tuesdays: 15:00 - 17:00;
Classroom: Block: C, sala: 100-A.
Bibliographic references
Main textbook
LAX, P. Linear algebra and its applications. Pure and applied mathematics: A Wiley series of texts and monographs. 2007.
Other books
OLIVER, P. J; SHAKIBAN, C; SHAKIBAN, C. Applied linear algebra. Upper Saddle Rier, NJ: Prentice Hall, 2006;
SERRE, D. Matrices: Theory & Application. L'Ecole Normale Supérieure de Lyon, 2001;
STRANG, G. Linear algebra and learning from data. Cambridge Wellesley-Cambridge Press, 2019.
Discipline content
Fundamentals of linear algebra: Linear spaces, isomorphisms, basis, dimension, canonical isomorphism, quotient space;
Duality: Dual space and Riesz's lemma;
Linear mappings and dimension theorem;
Matrices: change of basis and linear mapping;
Trace and determinant and their properties;
Spectral theory: Eigenvalues and eigenvectors;
Euclidean structures: inner dot, orthonormal basis, Gram-Schmidt decomposition, orthogonal projection and isometries;
Spectral theory for self-adjoint mappings;
Matrix's Inequalities;
Decomposition in singular values;
Discrete Fourier transform and fast Fourier transform;
Linear normed spaces;
Norms of matrices;
Spectral radius;
Condition number;
Topics of linear algebra in Data Science.
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