Vectors

Summary

• If \(u_1,⋯,u_n\) are \(n\) real numbers then viewed as an ordered sequence it is called an \(n\) -tuple , denoted by \(u=\left( u_1,⋯,u_n \right)\) . The numbers \(u_1,⋯,u_n\) are called the coordinates or components of \(u\) .
• \(R^n\) is defined as the collection of all \(n\) -tuples.
• \(n\) -tuples are also called vectors or \(n\) - vectors or points in \(R^n\) .
• If \(u=\left( u_1,⋯,u_n \right)\) is a vector and \(c\) a constant then \(cu\) is defined as

\[cu=\left( cu_1,⋯,cu_n \right)\]

• If \(u=\left( u_1,⋯,u_n \right)\) and \(v=\left( v_1,⋯,v_n \right)\) are two vectors then \(u+v\) is defined as

\[u+v =\left( u_1+v_1,⋯,u_n+v_n \right)\]