Indeterminate System - Conditions Giving Rise To Indeterminacy

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:

    No great idea in its beginning can ever be within the law. How can it be within the law? The law is stationary. The law is fixed. The law is a chariot wheel which binds us all regardless of conditions or place or time.
    Emma Goldman (1869–1940)

    One cannot be a good historian of the outward, visible world without giving some thought to the hidden, private life of ordinary people; and on the other hand one cannot be a good historian of this inner life without taking into account outward events where these are relevant. They are two orders of fact which reflect each other, which are always linked and which sometimes provoke each other.
    Victor Hugo (1802–1885)

    Only the person who has experienced light and darkness, war and peace, rise and fall, only that person has truly experienced life.
    Stefan Zweig (18811942)