Vector Spaces Rank of matrix is the number of non zero rows in REF form. Alternatively rank of matrix is = total number of columns - total number of dependent columns. In the REF form, If a column of a matrix can be expressed in terms of other columns then it is a dependent vector. The vectors on the left most side with leading 1 at the col number position ( 1 at 1st row 1st col, 1 at 2nd row 2nd col, likewise) then such columns are linearly independent columns. For linerarly independence a1v1+a2v2+a3v3=0 where v1,v2,v3 are vectors and a1,a2,a3 are scalars. Span of a vector space is all the possible vectors which can be formed using the basis vectors. Basis vectors are linearly independent vectors which can span the vector space. Column space is all possible set of vectors formed by the column vectors. Row space is all possible set of vectors formed by the row vectors. Dimension of a row space or column space is equal to its rank. Null space or kernel of a matrix is any vector x which ...
Comments
Post a Comment