# Linear Algebra Basis

### The book begins with systems of linear equations then covers matrix algebra before taking up finite dimensional vector spaces in full generality. Linear algebra basis. To say that it was drastically different and more difficult from my first lin al textbook would be an understatement. A basis b of a vector space v over a field f such as the real numbers r or the complex numbers c is a linearly independent subset of v that spans vthis means that a subset b of v is a basis if it satisfies the two following conditions. In this course on linear algebra we look at what linear algebra is and how it relates to vectors and matrices. We will begin our journey through linear algebra by defining and conceptualizing what a vector is rather than starting with matrices and matrix operations like in a more basic algebra course and defining some basic operations like addition subtraction and scalar multiplication. Equivalently a subset s v is a basis for v if any.

This section contains a complete set of video lectures on linear algebra along with transcripts and related resource files. Linear algebra from imperial college london. I will admit at first i loathed hoffman and kunze. Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations. Linear algebra jim hefferon third edition httpjoshuasmcvtedulinearalgebra.

For every finite subset b 1 b n of b and every a 1 a n in f if a 1 b 1 a n b n. Typically such a student will have taken calculus but this is not a prerequisite. I used this book in a linear algebra ii course. Let v be a vector space. The linear independence property.

A first course in linear algebra is an introductory textbook designed for university sophomores and juniors. Reviewed by douglas farenick university of regina. Mathematics for machine learning.