N*L] may be represented as a sequence of column vector
Consider 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
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
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
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