Linear Algebra Dimension
This note covers the following topics.
Linear algebra dimension. Equivalently b is a basis if its elements are. 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. Lets get our feet wet by thinking in terms of vectors and spaces. This section contains a complete set of video lectures on linear algebra along with transcripts and related resource files.
Despite two linear algebra classes my knowledge consisted of matrices determinants eigen something something. 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. In linear algebra the quotient of a vector space v by a subspace n is a vector space obtained by collapsing n to zero. Dimension theorem any vector space v has a basis. To say that it was drastically different and more difficult from my first lin al textbook would be an understatement.
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. 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. Name the course linear algebra but focus on things called matrices and vectors teach concepts like rowcolumn order with mnemonics instead. 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.
Linear algebra jim hefferon third edition httpjoshuasmcvtedulinearalgebra. The space obtained is called a quotient space and is denoted vn read v mod n or v by n.