Linear Algebra as an Introduction to Abstract Mathematics

DOI10.1142/9808zbMath1339.15001OpenAlexW2489339293MaRDI QIDQ3462584

Isaiah Lankham, Anne Schilling, Bruno Nachtergaele

Publication date: 15 January 2016

Full work available at URL: https://semanticscholar.org/paper/58fc068c41c90ce7774289b9ef550f896dc7d490

zbMATH Keywords

normeigenvaluelinear transformationsingular value decompositioneigenvectortextbookinvariant subspaceGram-Schmidt orthogonalizationHermitian operatorGaussian eliminationfundamental theorem of algebradeterminantlinear equationvector spaceinner product spacebasesorthogonalityrangediagonalizationunitary operatornormal operatorspositive operatorsnull spaceLU-factorization

Mathematics Subject Classification ID

Factorization of matrices (15A23) Determinants, permanents, traces, other special matrix functions (15A15) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Linear transformations, semilinear transformations (15A04) Direct numerical methods for linear systems and matrix inversion (65F05) Vector spaces, linear dependence, rank, lineability (15A03) Linear equations (linear algebraic aspects) (15A06) Canonical forms, reductions, classification (15A21) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra (15-01) Orthogonal matrices (15B10)

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