The concatenation of vectors can be understood in two distinct ways; either as a generalization of the above operation for numbers or as a concatenation of lists.
Given two vectors in, concatenation can be defined as
In the case of vectors in, this is equivalent to the above definition for numbers. The further extension to matrices is trivial.
Since vectors can be viewed in a certain way as lists, concatenation may take on another meaning. In this case the concatenation of two lists (a1, a2, ..., an) and (b1, b2, ..., bn) is the list (a1, a2, ..., an, b1, b2, ..., bn). Only the exact context will reveal which meaning is intended.
Read more about this topic: Concatenation (mathematics)
Famous quotes containing the word extension:
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (16231662)