This note covers the following topics: Linear Algebra, Matrix Algebra,
Homogeneous Systems and Vector Subspaces, Basic Notions, Determinants and
Eigenvalues, Diagonalization, The Exponential of a Matrix, Applications,Real
Symmetric Matrices, Classification of Conics and Quadrics, Conics and the Method
of Lagrange Multipliers, Normal Modes.
This note covers the following topics: Vector Spaces, Bases, Linear
Maps, Matrices and Linear Maps, Direct Sums, Affine Maps, The Dual Space,
Duality, Gaussian Elimination, LU, Cholesky, Echelon Form, Determinants, Vector
Norms and Matrix Norms, Eigenvectors and Eigenvalues, Iterative Methods for
Solving Linear Systems, Euclidean Spaces, Hermitian Spaces, Spectral Theorems,
The Finite Elements Method, Singular Value Decomposition and Polar Form,
Applications of SVD and Pseudo-Inverses, Annihilating Polynomials, Differential
Calculus, Schur Complements and Applications, Linear Programming and Duality,
Hilbert Spaces, Soft Margin Support Vector Machines.
This book is
addressed primarely to second and third year college engineering students who
have already had a course in calculus and analytic geometry. It is the result of
lecture notes given by the author at Arkansas Tech University. Topics covered
includes: Linear Systems of Equations, Matrices, Determinants, The Theory of
Vector Spaces, Eigenvalues and Eigenvectors, Linear Transformation.
This note explains
the following topics: Vector spaces, The field of complex numbers, Linear maps,
Subspaces, Matrices, Linear independence and dimension, Ranks, Linear maps and
matrices, Determinants, Eigenvalues and Eigenvectors.
This textbook is meant to be a
mathematically complete and rigorous introduction to abstract linear algebra for
undergraduates, possibly even first year students, specializing in mathematics.
Author tried very hard to emphasize the fascinating and important interplay
between algebra and geometry.
This book explains the following topics related to
Linear Algebra: Number systems and fields, Vector spaces, Linear independence,
spanning and bases of vector spaces, Subspaces, Linear transformations,
Matrices, Linear transformations and matrices, Elementary operations and the
rank of a matrix, The inverse of a linear transformation and of a matrix, Change
of basis and equivalent matrices.
This book is not a ”traditional” book in the sense that it does not include
any applications to the material discussed. Its aim is solely to learn the basic
theory of linear algebra within a semester period. Topics covered includes: Linear Systems, Matrices,
Determinants, The Theory of Vector Spaces, Eigenvalues and Diagonalization and