Eigenvalues and eigenvectors of matrices and linear operators are fundamental in mathematics. This short booklet is intended to be a self-contained treatment of how to determine the eigenvalues and... More > eigenvectors of a square matrix with real entries. It also includes a treatment on diagonalization: how to determine if a square matrix is similar to a diagonal matrix and how to find a diagonalizing matrix.
It includes all the necessary background material and algorithms for computing the characteristic polynomial, eigenvalues and eigenspaces of a square matrix: how to solve linear systems using matrices, how to find a basis for the null space of a matrix, how to invert a matrix and how to compute a determinant. In the interest of making it entirely self-contained each section begins with a review of the relevant definitions.< Less

Eigenvalues and eigenvectors of matrices and linear operators are fundamental in mathematics. This short booklet is intended to be a self-contained treatment of how to determine the eigenvalues and... More > eigenvectors of a square matrix with real entries. It also includes a treatment on diagonalization: how to determine if a square matrix is similar to a diagonal matrix and how to find a diagonalizing matrix.
It includes all the necessary background material and algorithms for computing the characteristic polynomial, eigenvalues and eigenspaces of a square matrix: how to solve linear systems using matrices, how to find a basis for the null space of a matrix, how to invert a matrix and how to compute a determinant. In the interest of making it entirely self-contained each section begins with a review of the relevant definitions.< Less

Linear Algebra by Jim Hefferon is released under the GNU Free Documentation license. Electronic copies may be downloaded for free. Hardcover copies are available for the cost of manufacturing (the... More > publisher receives no additional revenue). The book covers the material of a first undergraduate Linear Algebra course. The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Prerequisites: a semester of calculus. Students with three semesters of calculus can skip a few sections. The approach is developmental. It does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class.< Less

Linear Algebra by Jim Hefferon is released under the GNU Free Documentation license. Electronic copies may be downloaded for free. Hardcover copies are available for the cost of manufacturing (the... More > publisher receives no additional revenue). The book covers the material of a first undergraduate Linear Algebra course. The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Prerequisites: a semester of calculus. Students with three semesters of calculus can skip a few sections. The approach is developmental. It does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class.< Less

Answers to exercises presented in Linear Algebra by Jim Hefferon.
This book is released under the GNU Free Documentation license. Electronic copies may be downloaded for free. Paperback copies are... More > available for the cost of manufacturing (the publisher receives no additional revenue).< Less

Answers to exercises presented in Linear Algebra by Jim Hefferon.
This book is released under the GNU Free Documentation license. Electronic copies may be downloaded for free. Paperback copies are... More > available for the cost of manufacturing (the publisher receives no additional revenue).< Less

Abstract. A unique fundamental and universal description of objective reality compatible with classical physics (i. e. using the mathematical and conceptual framework of quantum theory) is still not... More > possible. Classical physics and quantum physics differs drastically. One striking aspect of the difference between quantum physics and classical physics is whether a quantum mechanical object do possess exact, definite and simultaneous values (i. e. for its position and momentum at the same time or at a concrete quantum state).
This publication will provide the prove, that it is possible to assign exact, definite and simultaneous values even to quantum mechanical observables.< Less

This text provides the reader with a solid foundation of the fundamental operations and concepts of matrix algebra. The topics include systems of linear equations, matrix arithmetic, transpose,... More > trace, determinant, eigenvalues/vectors, and linear transformations, focusing largely on transformations of the Cartesian plane.
The text is designed to be easily read, written in a casual style. Key concepts are explained, but rigorous proofs are omitted. Numerous examples are provided to illuminate new ideas and provide practice. Each section ends with exercises (with answers to odd questions appearing in the back).
The text is currently in use by Cadets of the Virginia Military Institute, and is appropriate for undergraduates in mathematics and the sciences, as well as advanced high school students.< Less

This text provides the reader with a solid foundation of the fundamental operations and concepts of matrix algebra. The topics include systems of linear equations, matrix arithmetic, transpose,... More > trace, determinant, eigenvalues/vectors, and linear transformations, focusing largely on transformations of the Cartesian plane.
The text is designed to be easily read, written in a casual style. Key concepts are explained, but rigorous proofs are omitted. Numerous examples are provided to illuminate new ideas and provide practice. Each section ends with exercises (with answers to odd questions appearing in the back).
The text is currently in use by Cadets of the Virginia Military Institute, and is appropriate for undergraduates in mathematics and the sciences, as well as advanced high school students.< Less