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Teacher
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PONTECORVO MASSIMILIANO
(syllabus)
Vectors in Euclidean Space. Reference and co-ordered systems. Orthogonal poijections, scalar, vector and mixed product. Parametric and Cartesian equations of lines and planes.
Linear systems. Linear equations, column vectors and matrices. Gauss elimination method: rank of a matrix, Cramer and Rouch ́e-Capelli theorems.
Algebra of Matrices. Sum and product for a scalar. Produced rows by columns. Invertible matrices, transposed matrix and symmetric matrices. The Gauss-Jordano algorithm for calculating the inverse. LU factorization. Product of block matrices.
Vector spaces and linear applications. Examples of vector spaces and linear applications. Generators and bases. Core, image. Linear independence and size; rank of a matrix. Nullity theorem plus rank and Grassmann's formula.
Determinant of a matrix and Gauss moves. Developments of Laplace. Binet's theorem.
Eigenvalues and eigenvectors. The characteristic polynomial of a linear operator. Similar matrices.
Scalar products. Schwartz inequality, orthogonal bases and matrices. Orthogonal projections and Grahm-Schmidt algorithm.
Quadratic shapes and self-added operators. The spectral theorem, quadratic forms. Classification of conics and quadrics.
(reference books)
Enrico Schlesinger, Algebra lineare e geomegtria. Zanichellii, (2017).
Luca Mauri, Enrico Schlesinger, Esercizi di algebra lineare e geomegtria. Zanichellii, (2020).
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Università Roma Tre