Linear Algebra Change Of Basis
Typically such a student will have taken calculus but this is not a prerequisite.
Linear algebra change of basis. This course covers matrix theory and linear algebra emphasizing topics useful in other disciplines such as physics economics and social sciences natural sciences and engineering. Elements of a vector space may have various nature. The book begins with systems of linear equations then covers matrix algebra before taking up finite dimensional vector spaces in full generality. Here is a set of notes used by paul dawkins to teach his algebra course at lamar university. For example they can be sequences functions polynomials or matriceslinear algebra is concerned with properties common to all vector spaces.
This note covers the following topics. The first four axioms mean that v is an abelian group under addition. 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. Included area a review of exponents radicals polynomials as well as indepth discussions of solving equations linear quadratic absolute value exponential logarithm and inqualities polynomial rational absolute value functions definition notation evaluation inverse functions graphing. Linear algebra matrix algebra homogeneous systems and vector subspaces basic notions determinants and eigenvalues diagonalization the exponential of a matrix applicationsreal symmetric matrices classification of conics and quadrics conics and the method of lagrange multipliers normal modes.
I will admit at first i loathed hoffman and kunze. I used this book in a linear algebra ii course. In mathematics a set b of elements vectors in a vector space v is called a basis if every element of v may be written in a unique way as a finite linear combination of elements of bthe coefficients of this linear combination are referred to as components or coordinates on b of the vector. The elements of a basis are called basis vectors. Equivalently b is a basis if its elements are.
It parallels the combination of theory and applications in professor strangs textbook introduction to linear algebra. A first course in linear algebra is an introductory textbook designed for university sophomores and juniors. Well lets try this course format. To say that it was drastically different and more difficult from my first lin al textbook would be an understatement.