Vector spaces and subspaces solved examples pdf

4.1 Vector Spaces and Subspaces 1. Notation: The symbol;means "the empty set". The symbol2means "is an element of". The symbolµmeans "is a subset of". The symbolsfxjP(x)gmean "the set ofxsuch thatxhas the propertyP. R = "the real numbers". Elements of R are called scalars. 2. The definition of an abstract vector space and examples. Vector Spaces and SubSpaces Linear Algebra MATH 2076 Section 4.1.B Vector Spaces 20 February 2017 1 / 1. Examples of Vector Spaces Some simple examples: 1 Rn is a vector space ^ 2 Rm n is the vector space of all m n matrices (given m n matrices A and B, we know what A+ B and sA are, right?)