Matrices: Lecture Notes

Matrix Properties / Features

Generic matrices whose size is unspecified (or given by $n \times m$) can be created using ellipses ($\dots$). For example:

15. $A = \begin{bmatrix} a_{1,1} & a_{1,2} & a_{1,3} & \dots & a_{1,m} \\ a_{2,1} & a_{2,2} & a_{2,3} & \dots & a_{2,m} \\ a_{3,1} & a_{3,2} & a_{3,3} & \dots & a_{3,m} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ a_{n,1} & a_{n,2} & a_{n,3} & \dots & a_{n,m} \end{bmatrix}$

or for $n \times n$:

16. $S = \begin{bmatrix} s_{1,1} & s_{1,2} & s_{1,3} & \dots & s_{1,n} \\ s_{2,1} & s_{2,2} & s_{2,3} & \dots & s_{2,n} \\ s_{3,1} & s_{3,2} & s_{3,3} & \dots & s_{3,n} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ s_{n,1} & s_{n,2} & s_{n,3} & \dots & s_{n,n} \end{bmatrix}$

$A = \begin{bmatrix} a_{1,1} & a_{1,2} & a_{1,3} & \dots & a_{1,m} \\ a_{2,1} & a_{2,2} & a_{2,3} & \dots & a_{2,m} \\ a_{3,1} & a_{3,2} & a_{3,3} & \dots & a_{3,m} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ a_{n,1} & a_{n,2} & a_{n,3} & \dots & a_{n,m} \end{bmatrix}$