You can teach a course that will give their students exposure to linear algebra. In their first brush with the topic, your students can work with the Euclidean space and the matrix. In contrast, this course will emphasize the abstract vector spaces and linear maps. Bold title of this book deserves an explanation. Almost all linear algebra books use determinants to prove that each linear op-erator on a finite dimensional vector space has a complex eigenvalue.
Linear algebra is the language of chemometrics. One cannot expect to truly understand most
chemometric techniques without a basic understanding of linear algebra. This article
reviews the basics of linear algebra and provides the reader with the foundation required for
understanding most chemometrics literature. It is presented in a rather dense fashion: no
proofs are given and there is little discussion of the theoretical implications of the theorems
and results presented.
Here are my online notes for my Linear Algebra course that I teach here at Lamar University. Despite the fact that these are my “class notes” they should be accessible to anyone wanting to learn Linear Algebra or needing a refresher. These notes do assume that the reader has a good working knowledge of basic Algebra.
an one learn linear algebra solely by solving problems? Paul Halmos thinks so, and you will too once you read this book. The Linear Algebra Problem Book is an ideal text for a course in linear algebra. It takes the student step by step from the basic axioms of a field through the notion of vector spaces, on to advanced concepts such as inner product spaces and normality. All of this occurs by way of a series of 164 problems, each with hints and, at the back of the book, full solutions. This book is a marvelous example of how...
This is a book on linear algebra and matrix theory. While it is self contained, it will work
best for those who have already had some exposure to linear algebra. It is also assumed that
the reader has had calculus. Some optional topics require more analysis than this, however.
I think that the subject of linear algebra is likely the most significant topic discussed in
undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying
so many different topics. Linear algebra is essential in analysis, applied math, and even in
Linear algebra occupies a central place in modern mathematics. Also, it is a beautiful and mature field of mathematics, and mathematicians have developed highly effective methods for solving its problems. It is a subject well worth studying for its own sake. This book contains selected topics in linear algebra, which represent the recent contributions in the most famous and widely problems. It includes a wide range of theorems and applications in different branches of linear algebra, such as linear systems, matrices, operators, inequalities, etc.
Lecture "Linear algebra - Chapter 4: Vector space" provides learners with the knowledge: Definition and examples, linear independence, rank of vectors, basic and dimension, subspaces. Invite you to refer to the disclosures.
Lecture "Linear algebra - Chapter 5: Linear transformation" provides learners with the knowledge: Definition and examples, the Kernel and Image of linear transformation, the Matrix of a linear transformation, the Matrix of a linear transformation, similarity. Invite you to refer to the disclosures.
Lecture "Linear algebra - Chapter 5: Eigenvalues and Eigenvectors" provides learners with the knowledge: Eigenvalues and eigenvectors, diagonalization, eigenvectors and linear transformations, hermitian matrices,... Invite you to refer to the disclosures.
Lecture "Linear algebra - Chapter 0: Complex Numbers" provides learners with the knowledge: The standard form, the trigonometric form, the exponential form, the Power of complex numbers, the Roots of complex numbers, the Fundamental Theorem of Algebra. Invite you to refer to the disclosures.
Lecture "Linear algebra - Chapter 1: Matrix Algebra" provides learners with the knowledge: Elementary row operations, elementary row operations, matrix operations, a rank of matrix, an inverse of matrix. Invite you to refer to the disclosures.
Lecture "Linear algebra - Chapter 4: Vector space" provides learners with the knowledge: Coordinates of a vector, subspaces, the intersection and sum of subspaces. Invite you to refer to the disclosures.
Lecture "Linear algebra - Chapter 5: The Orthogonality and Least Squares" provides learners with the knowledge: The Scalar Product in R, orthogonal subspaces, orthonormal set, the gram schmidt orthogonalization process, inner product spaces, least square problem. Invite you to refer to the disclosures.
(BQ) Part 1 book "Elementary linear algebra" has contents: Systems of linear equations and matrices, determinants, vectors in 2 space and 3 space, euclidean vector spaces, general vector spaces, inner product spaces,... and other contents.