Linear Algebra Dimension
Name the course linear algebra but focus on things called matrices and vectors teach concepts like rowcolumn order with mnemonics instead.
Linear algebra dimension. This section contains a complete set of video lectures on linear algebra along with transcripts and related resource files. All bases for v are of the same cardinality. The dimension of a vector space v denoted dimv is the cardinality of its bases. Equivalently b is a basis if its elements are. Despite two linear algebra classes my knowledge consisted of matrices determinants eigen something something.
To say that it was drastically different and more difficult from my first lin al textbook would be an understatement. I will admit at first i loathed hoffman and kunze. 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. Lets get our feet wet by thinking in terms of vectors and spaces. It parallels the combination of theory and applications in professor strangs textbook introduction to linear algebra.
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. Dimension theorem any vector space v has a basis. This note covers the following topics. Linear algebra jim hefferon third edition httpjoshuasmcvtedulinearalgebra. In linear algebra the quotient of a vector space v by a subspace n is a vector space obtained by collapsing n to zero.
I used this book in a linear algebra ii course. 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.