# column rank

## column rank

[′käl·əm ‚raŋk]
(mathematics)
The number of linearly independent columns of a matrix; the dimension of the image of the corresponding linear transformation.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
The column rank of A is the generator dimension for the column space of A.
However, there are two distinct limitations in this algorithm: 1) The successful decoding ratio is entirely dependent on the rank of the random matrix (the coefficient matrix of all the collected encoded packets).Only when the random matrix is full column rank, can user decode data successfully and recover all the source packets at one time.
is of full column rank. Due to [[A.bar].sub.22] being nonsingular,
A matrix m has full column rank if mm is invertible.
It is shown that C is full column rank because the system is observable while B is full column rank because the system is controllable.
where x(t) [member of] [R.sup.n] is state vector, u(t) [member of] [R.sup.m] is control input, and y(t) [member of] [R.sup.l] is controlled output, E [member of] [R.sup.nxn] is singular matrix with rank E = [n.sub.1] [less than or equal to] n, and B [member of] [R.sup.nxm], C [member of] [R.sup.lxn] are full column rank and full row rank, respectively.
We denote [j.sub.k] = min{j | j [member of] I([x.sup.k])} and use the following pivoting operation to generate the index set [[??].sup.k] such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] has full column rank, so vectors {[g.sub.j]([x.sup.k]), j [member of] [[??].sub.k]} are linearly independent.
The system (1) is said to be left invertible if and only if its transfer function matrix (13) has full column rank.
The maximal number of right independent columns of A will be called right column rank of A.
A system is observable if [[GAMMA].sub.0] has full column rank n and, in turn, a system is controllable if [[GAMMA].sub.c] has full row rank.
P is called column reduced, if there exists a permutation matrix T, such that P = (0, [P.sub.1])T, where [[Gamma].sub.c]([P.sub.1]) has full column rank.
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