Lecture 7 (Mar 2)
Construction of the inverse of an invertible matrix.
Vector space. Definition.
Note: In the lecture we wanted to know if it is possible to have a vector space with only finite number of elements. It is actually possible. For example, we consider the set V={the zero vector in the standard Euclidean space R^n}. It forms a vector space under standard addition and scalar multiplication. A related question is, if it is possible to find a vector space which is (1) a subset of the Euclidean space under usual addition and scalar multiplication, and (2) with more than one but finitely many elements? The question is no. But it is actually possible to construction a (nontrivial) vector space with finite number of elements and, unfortunately, this will be a topic in an algebra class.
Vector space. Definition.
Note: In the lecture we wanted to know if it is possible to have a vector space with only finite number of elements. It is actually possible. For example, we consider the set V={the zero vector in the standard Euclidean space R^n}. It forms a vector space under standard addition and scalar multiplication. A related question is, if it is possible to find a vector space which is (1) a subset of the Euclidean space under usual addition and scalar multiplication, and (2) with more than one but finitely many elements? The question is no. But it is actually possible to construction a (nontrivial) vector space with finite number of elements and, unfortunately, this will be a topic in an algebra class.
Comments
Post a Comment