A simple 3 times 2 matrix

Matrices > Basics > Example

Consider the 3 times 2 matrix

A = left( begin{array}{cc} 3 & 4.5 2 & 1.2 -0.1 & 8.2 end{array}right) .

The matrix can be interpreted as the collection of two column vectors: A = (a_1,a_2), where a_j's contain the columns of A:

a_1 = left( begin{array}{c} 3 2 -0.1 end{array}right), ;; a_2 = left( begin{array}{c} 4.5 1.2 8.2 end{array}right), ;;

Geometrically, A represents 2 points in a 3-dimensional space.

 

Alternatively, we can interpret A as a collection of 3 row vectors in mathbf{R}^2:

A = left( begin{array}{c} b_1^T b_2^T b_3^T end{array}right) ,

where b_i's, i=1,2,3 contain the rows of A:

b_1 = left( begin{array}{c} 3 4.5 end{array}right), ;; b_2 = left( begin{array}{c} 2 1.2 end{array}right), ;; b_3 = left( begin{array}{c} -0.1 8.2 end{array}right) .

Geometrically, A represents 3 points in a 2-dimensional space.