Examples of Basic Coordinate Vectors

Example

\(\RNrSpc{3}\) has three basic coordinate vectors.

Explanation

  • The first basic coordinate vector of \(\RNrSpc{3}\) is \(\mathbf{e}_1\DefEq (1,0,0)\)
  • The second basic coordinate vector of \(\RNrSpc{3}\) is \(\mathbf{e}_2\DefEq (0,1,0)\)
  • The third basic basic coordinate vector of \(\RNrSpc{3}\) is \(\mathbf{e}_3\DefEq (0,0,1)\)

In the physics literature these are often written as

\(\mathbf{i}\DefEq \mathbf{e}_1,\qquad \mathbf{j}\DefEq \mathbf{e}_2,\quad \text{and}\quad \mathbf{k}\DefEq \mathbf{e}_3\)

Example

\(\RNrSpc{4}\) has four basic coordinate vectors

Explanation

  • The first basic coordinate vector of \(\RNrSpc{4}\) is \(\mathbf{e}_1\DefEq (1,0,0,0)\)
  • The second basic coordinate vector of \(\RNrSpc{4}\) is \(\mathbf{e}_2\DefEq (0,1,0,0)\)
  • The third basic basic coordinate vector of \(\RNrSpc{4}\) is \(\mathbf{e}_3\DefEq (0,0,1,0)\)
  • The fourth basic basic coordinate vector of \(\RNrSpc{4}\) is \(\mathbf{e}_4\DefEq (0,0,0,1)\)