May 3, 2015 · You may prove that these two definitions are equivalent. However, what is more important than that is to understand the difference between these two definitions. In fact they …

Sep 8, 2011 · Right, and that is my point; often systems of equations to be solved are described as systems of linear equations, when the equations in the system are not those of linear …

Elementary Linear Algebra, Sixth Edition, By Larson, Edwards, and Falvo, chapter 4, section 4.4, Spanning Sets and Linear Independence, page# 211. It is not the book I am using but …

Aug 1, 2016 · Linear Algebra is the study of linear maps on finite dimensional vector spaces; the original motivation and first application of this is solving systems of linear equations.

Aug 26, 2024 · So, a linear combination is always a finite linear combination. The basis set will still be an infinite collection, but only a finite number of them will have nonzero coefficients in …

Jan 27, 2016 · I hear so many terms involving the word "linear". Linear function, linear equation, linear system, linear operator, linear transformation, linear mapping, linear space, linear …

The set of vectors are called the base of the vector space. How to make this notion formal? For that, we use the theory of linear algebra. We define what is a vector and what we mean by a …

Sep 23, 2016 · The reason is that physicists care about the definition of a vector. In linear algebra, the definition of a vector is irrelevant, what is important is the definition of a vector space.

Apr 6, 2020 · Rapidly, for your second question, the polyhedron can be infinite from the definition. It might be surprising at first glance but from a mathematical point of view it is not a problem.

Dec 14, 2022 · I don't know of any linear algebra books that define the determinant as a volume, and I'm not sure there are many out there. If the book is focused on the computational side of …