 ## Category: DEFAULT

1 VECTOR SPACES AND SUBSPACES What is a vector? Many are familiar with the concept of a vector as: • Something which has magnitude and direction. • an ordered pair or triple. • a description for quantities such as Force, velocity and acceleration. Such vectors belong to the foundation vector space - Rn - of all vector spaces. The. A vector space V over a ﬁeld K is said to be trivial if it consists of a single element (which must then be the zero element of V). A vector space with more than one element is said to be non-trivial. Examples of Vector Spaces Example. The set of all vectors in 3-dimensional Euclidean space is a real vector space: the vector. What is a Vector Space? Geo rey Scott These are informal notes designed to motivate the abstract de nition of a vector space to my MAT students. I had trouble understanding abstract vector spaces when I took linear algebra { I hope these help! Why we need vector spaces By now in your education, you’ve learned to solve problems like the one.