This introduction to linear algebra gives attention to the skills of constructing, reading and writing mathematical proofs. The book also provides flexibility with the applications of linear algebra. It covers a range of topics from the elementary concepts to non-trivial, important results. Its gradual, methodical building of concepts begins with vectors and matrices, and results in abstract algebra.
This introduction to linear algebra gives attention to the skills of constructing, reading and writing mathematical proofs. The book also provides flexibility with the applications of linear algebra. It covers a range of topics from the elementary concepts to non-trivial, important results. Its gradual, methodical building of concepts begins with vectors and matrices, and results in abstract algebra.
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Für höhere Schule und Studium
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ISBN-13
978-0-534-17964-9 (9780534179649)
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Schweitzer Klassifikation
Vectors and matrices; Fundamental operations with vectors; The dot product; An introduction to proofs; Fundamental operations with matrices; Matrix multiplication; Systems of linear equations; Solving systems of linear equations; Equivalent systems and rank; Row space of a matrix; Inverses of matrices; Elementary matrices; Determinants; Introduction to determinants; Using row reduction to calculate determinants; Finite dimensional vector spaces; Subspaces; Span; Linear independence; Basis and dimension; Constructing special bases; Co-ordinatization; Linear transformations and orthogonality; Introduction to linear transformations; The matrix of a linear transformation; The dimension theorem; Isomorphism; Orthogonality and the Gram-Schmidt process; Orthogonal complements; Eigenvalues and Eigenvectors; Introduction to Eigenvalues; Diagonalization; Orthogonal diagonalization; Complex vector spaces; Products; Complex vector spaces; Inner product spaces; Applications; Graph theory; Ohm's law; Least-squares approximations; Markov chains; Hill substitution: an introduction to coding theory; Function spaces; Rotation of axes; Differential equations; Quadratic forms; Numerical methods for solving systems; LDU decomposition; The power method for finding Eigenvalues.
