# Linear Algebra Dimension

### This section contains a complete set of video lectures on linear algebra along with transcripts and related resource files. Linear algebra dimension. 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. In linear algebra the quotient of a vector space v by a subspace n is a vector space obtained by collapsing n to zero. Despite two linear algebra classes my knowledge consisted of matrices determinants eigen something something. Linear algebra jim hefferon third edition httpjoshuasmcvtedulinearalgebra. It parallels the combination of theory and applications in professor strangs textbook introduction to linear algebra.

To say that it was drastically different and more difficult from my first lin al textbook would be an understatement. All bases for v are of the same cardinality. 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. Dimension theorem any vector space v has a basis. I used this book in a linear algebra ii course.

This note covers the following topics. I will admit at first i loathed hoffman and kunze. The dimension of a vector space v denoted dimv is the cardinality of its bases. Well lets try this course format. Name the course linear algebra but focus on things called matrices and vectors teach concepts like rowcolumn order with mnemonics instead.

The space obtained is called a quotient space and is denoted vn read v mod n or v by n. Lets get our feet wet by thinking in terms of vectors and spaces.