Conditions Giving Rise To Indeterminacy
In linear systems, indeterminacy occurs if and only if the number of independent equations (the rank of the augmented matrix of the system) is less than the number of unknowns and is the same as the rank of the coefficient matrix. For if there are at least as many independent equations as unknowns that will eliminate any stretches of overlap of the equations' surfaces in the geometric space of the unknowns (aside from possibly a single point); and if the rank of the augmented matrix exceeds (necessarily by one if at all) the rank of the coefficient matrix then the equations jointly contradict each other.
Read more about this topic: Indeterminate System
Famous quotes containing the words conditions, giving and/or rise:
“Each victim of suicide gives his act a personal stamp which expresses his temperament, the special conditions in which he is involved, and which, consequently, cannot be explained by the social and general causes of the phenomenon.”
—Emile Durkheim (1858–1917)
“It is old age, rather than death, that is to be contrasted with life. Old age is life’s parody, whereas death transforms life into a destiny: in a way it preserves it by giving it the absolute dimension. ... Death does away with time.”
—Simone De Beauvoir (1908–1986)
“I don’t say ‘tis impossible for an impudent man not to rise in the world, but a moderate merit with a large share of impudence is more probable to be advanced than the greatest qualifications without it.”
—Mary Wortley, Lady Montagu (1689–1762)