Algebra Of Linear Transformations Research Articles

Linear algebra with applications

1. Linear systems: Introduction to Linear Systems. Gauss Elimination. Numerical Solutions. 2. Vectors: Vector Operations. Dot Product. Span. Linear Independence. The Product [Ax]. Cross Product. Lines, Planes, and Hyperplanes. 3. Matrices: Matrix Operations. Matrix Inverse. Elementary and Invertible Matrices. LU Factorization. 4. Vector spaces: Subspaces of [R to the n Power]. Vector Spaces. Linear Independence Bases. Dimension. Coordinate Vectors and Change of Basis. Rank and Nullity. Applications to Coding Theory. 5. Linear transformations: Matrix Transformations. Linear Transformations. Kernel and Range. The Matrix of a Linear Transformation. The Algebra of Linear Transformations. 6. Determinants: Determinants Cofactor Expansion. Properties of Determinants. The Adjoint Cramer's Rule. Determinants with Permutations. 7. Eigenvalues and eigenvectors: Eigenvalues and Eigenvectors. Diagonalization. Approximations of Eigenvalues and Eigenvectors. Applications to Dynamical Systems. Applications to Markov Chains. 8. Dot and inner products: Orthogonal Sets and Matrices. Orthogonal Projections Gram-Schmidt Process. The QR Factorization. Least Squares. Orthogonalization of Symmetric Matrices. Quadratic Forms and Conic Sections. The Singular Value Decomposition (SVD). Inner Products. Appendices: Answers to selected exercises Each chapter concludes with Applications, Mini-Projects, and Computer Exercises.

Methoden der mathematischen Physik

THESE two volumes are photo-lithoprints of the second edition of Vol. 1, issued in 1930, and Vol. 2, issued in 1937. The first volume contains seven chapters as follows: 1, the algebra of linear transformations and quadratic forms; 2, the development of an arbitrary function in series; 3, the theory of linear integral equations; 4, the basic principles of the calculus of variations; 5, the oscillation and eigenvalue problems of mathematical physics; 6, application of the calculus of variations to eigenvalue problems; 7, special functions defined by eigenvalue problems. Methoden der mathematischen Physik Von Prof. R. Courant Prof. D. Hilbert. (Published and distributed in the Public Interest with the consent of the Alien Property Custodian under License No. A. 82.) Band 1. Zweite verbesserte Auflage. Pp. xv + 469. 8 dollars. Band 2. Pp. xiv + 549. 8 dollars. (New York: Interscience Publishers, Inc.; London: H. K. Lewis and Co., Ltd., 1931–1937.) 2 vols., 14 dollars.