Rank Finite Operator Linear (1 results)

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! The column rank of a matrixA is the maximal number of linearly independent columns of A. Likewisethe row rank is the maximal number of linearly independent rows of A.Since the column rank and the row rank are always equal, they are simplycalled the rank of A. More abstractly, it is the dimension of the imageof the linear transformation that is multiplication by A. For theproofs, see, e.g., Murase (1960), Andrea & Wong (1960), Williams& Cater (1968), Mackiw (1995). It is commonly denoted by eitherrk(A) or rank A. The rank of an m × n matrix is at most min(m, n). Amatrix that has a rank as large as possible is said to have full rank;otherwise, the matrix is rank deficient. More generally, if a linearoperator on a vector space (possibly infinite-dimensional) hasfinite-dimensional range (e.g., a finite rank operator), then the rankof the operator is defined as the dimension of the range.…