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With Robert Charles Thompson, he was the co-founder of the journal Linear and Multilinear Algebra, [2] whose first issue was published in 1973. [8] He was the section editor for linear algebra in Addison-Wesley's series Encyclopedia of mathematics and its applications. [9]
With respect to general linear maps, linear endomorphisms and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other part of mathematics.
Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States, [5] and builds on their understanding of arithmetic. The use of variables to denote quantities allows ...
Matrix Analysis and Applied Linear Algebra. Society for Industrial and Applied Mathematics (SIAM). ISBN 978-0-89871-454-8. Archived from the original on March 1, 2001. Poole, David (2006). Linear Algebra: A Modern Introduction (2nd ed.). Brooks/Cole. ISBN 0-534-99845-3. Anton, Howard (2005). Elementary Linear Algebra (Applications Version) (9th ...
Conversely, every line is the set of all solutions of a linear equation. The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding ...
Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis.
For many problems in applied linear algebra, it is useful to adopt the perspective of a matrix as being a concatenation of column vectors. For example, when solving the linear system =, rather than understanding x as the product of with b, it is helpful to think of x as the vector of coefficients in the linear expansion of b in the basis formed by the columns of A.