STAT312 Lecture : Column spaces, dimension, rank.pdf
5 Apr 2014
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From now on we work only with the vector space. R , and aim to relate matrices to (subspaces of) this vector space. Let be a vector subspace of r . ), called the column space (x)), whose dimension is called the rank of: the independent columns of x form a basis for. Rank can mean either row rank or column rank. Using 4) and 1), (ab) (b)). (a) has been shown. (ab) = (b0a0) A square, full rank matrix a has an inverse, i. e. a matrix b such that ab = ba = i . A [b1 b ] = [e1 e ] = i are all solvable (e1 = ). We write [b1 b ] = B, then ab = i and so a has a right in- verse, namely b. The matrix b is square, full rank (why?) and so it also has an inverse on the right: there is c with bc = i .
