N*L] may be represented as a sequence of

column vectorConsider the set A' of all d x (d +1) matrices such that each

column vector belongs to M and 0 is a convex combination of columns.

The axis can be represented as a unit

column vector u

Due to the associativity property of the matrix multiplication and interpreting o as the row vector and [XI] as the

column vector, one may rewrite this result as

Here y is a

column vector, and the prime symbol denotes the transpose.

which solution, in turn, is a

column vector of generalized coordinates [PHI](t) as a function of time, which uniquely determines the desired trajectory of the manipulator end-effector.

Let [omega] be the

column vector [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the matrix obtained from [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] by replacing its kth column with the column vecto [omega].

The 64 x 64 input binary matrix representing a letter is transformed into a 1 x 4096

column vector.

n]) and A is some m x n matrix of rank m [less than or equal to] n and b some m-dimensional

column vector, then

where Y is a 3 x 1

column vector that represents the citation ranks added to each document, M is the 3 x 3 link matrix (of relative citation frequencies), and R is the 3 x 1

column vector of initial ranks.

t,k] and therefore, the composition of the population in age a is described by the

column vector [X.

If F represents a

column vector of final demand values, sector-by-sector, while X represents a

column vector of output values, sector-by-sector, a fundamental relationship of input-output analysis is