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  • Book
    Emilio Bombardieri, Ettore Seregni, Laura Evangelista, Carlo Chiesa, Arturo Chiti, editors.
    Digital Access Springer 2018
  • Book
    by A.I. Kostrikin and Yu. I. Manin ; translated from the second Russian edition by M.E. Alferieff.
    Summary: This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metic, the theory of Hilbert polynomials, and projective and affine geometries. Unusual in its extensive use of applications in physics to clarify each topic, this comprehensice volume should be of particular interest to advanced undergraduates and graduates in mathematics and physics, and to lecturers in linear and multilinear algebra, linear programming and quantum mechanics. Nielsen 9782881246838 20160528

    Contents:
    Part 1 Linear spaces and linear mappings: linear spaces
    basis and dimension
    linear mappings
    matrices
    subspaces and direct sums
    quotient spaces
    duality
    the structure of a linear mapping
    the Jordan normal form
    normed linear spaces
    functions of linear operators
    complexification and decomplexification
    the language of categories
    the categorical properties of linear spaces. Part 2 Geometry of spaces with an inner product: on geometry
    inner products
    classification theorems
    the orthogonalization algorithm and orthogonal polynomials
    Euclidian spaces
    unitary spaces
    orthogonal and unitary operators
    self-adjoint operators
    self-adjoint operators in quantum mechanics
    the geometry of quadratic forms and the Eigenvalues of self-adjoint operators
    three-dimensional Euclidean space
    Minkowski space
    symplectic space
    Witt's theorem and Witt's group
    Clifford algebras. Part 3 Affine and projective geometry: affine spaces, affine mappings and affine coordinates
    affine groups
    affine subspaces
    convex polyhedra and linear programming
    affine quadratic functions and quadrics
    projective duality and projective quadrics
    projective groups and projections
    Desargues' and Pappus' configurations and classical projective geometry
    the Kahler metric
    algebraic varieties and Hilbert polynomials. Part 4 Multilinear algebra: tensor products of linear spaces
    canonical isomorphisms and linear mappings of tensor products
    the tensor algebra of a linear space
    classical notation
    symmetric tensors
    skew-symmetric tensors and the exterior algebra of a linear space
    exterior forms
    tensor fields
    tensor products in quantum mechanics. Nielsen 9782881246838 20160528
    Print c1989
  • Article
    Gailiunas P, Suthanthiran M, Person A, Carpenter CB, Garovoy MR.
    Transplant Proc. 1977 Dec;9(4):1823-5.
    Digital Access Access Options