# Linear Algebra Dimension

### All bases for v are of the same cardinality. Linear algebra dimension. To say that it was drastically different and more difficult from my first lin al textbook would be an understatement. This section contains a complete set of video lectures on linear algebra along with transcripts and related resource files. Name the course linear algebra but focus on things called matrices and vectors teach concepts like rowcolumn order with mnemonics instead. Despite two linear algebra classes my knowledge consisted of matrices determinants eigen something something. Well lets try this course format.

I will admit at first i loathed hoffman and kunze. Lets get our feet wet by thinking in terms of vectors and spaces. 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. The dimension of a vector space v denoted dimv is the cardinality of its bases. Dimension theorem any vector space v has a basis.

This note covers the following topics. The space obtained is called a quotient space and is denoted vn read v mod n or v by n. 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. I used this book in a linear algebra ii course.

It parallels the combination of theory and applications in professor strangs textbook introduction to linear algebra. In linear algebra the quotient of a vector space v by a subspace n is a vector space obtained by collapsing n to zero.