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