Matrix Analysis and Applied Linear Algebra

  title={Matrix Analysis and Applied Linear Algebra},
  author={Carl Dean Meyer},
Preface 1. Linear equations 2. Rectangular systems and echelon forms 3. Matrix algebra 4. Vector spaces 5. Norms, inner products, and orthogonality 6. Determinants 7. Eigenvalues and Eigenvectors 8. Perron-Frobenius theory of nonnegative matrices Index. 
Computational And Algorithmic Linear Algebra And N-Dimensional Geometry
Methods for Formulating Real World Problems Using Systems of Simultaneous Linear Equations Algorithms for Analyzing and Solving These Models Fundamental Concepts in N-Dimensional Geometry, Matrices
A Concise Text on Advanced Linear Algebra
Preface Notation and convention 1. Vector spaces 2. Linear mappings 3. Determinants 4. Scalar products 5. Real quadratic forms and self-adjoint mappings 6. Complex quadratic forms and self-adjoint
Matrices and Matrix Operations
In order to introduce the main ideas of Linear Algebra, we first study matrix algebra. So, the first thing we begin with is the following simple linear equation:
New matrix partial order based spectrally orthogonal matrix decomposition . Linear and Multilinear Algebra
We investigate partial orders on the set of complex square matrices and introduce a new order relation based on spectrally orthogonal matrix decompositions. We also establish the relation of this
On the equality of algebraic and geometric multiplicities of matrix eigenvalues
Applications of Matrices Multiplication to Determinant and Rotations formulas in $\setR^n$
This note deals with two topics of linear algebra. We give a simple and short proof of the multiplicative property of the determinant and provide a constructive formula for rotations. The derivation
Block Matrices in Linear Algebra
It is shown that linear algebra is best done with block matrices, and numerous examples suitable for classroom presentation are presented.
Analytic Results for the Eigenvalues of Certain Tridiagonal Matrices
The eigenvalues and eigenvectors are shown to be expressible in terms of solutions of a certain scalar trigonometric equation, and explicit solutions of this equation are obtained for several special cases.
Inequalities for Graph Eigenvalues
Preface 1. Introduction 2. Spectral radius 3. Least eigenvalue 4. Second largest eigenvalue 5. Other eigenvalues of the adjacency matrix 6. Laplacian eigenvalues 7. Signless Laplacian eigenvalues 8.
Basic Mathematics: Matrix Operations, Integration and Optimization
This chapter describes basic mathematical functions. It then gives some usual operations on matrices and the most usual decompositions. We also present a few numerical integration and differentiation