2.2.2 So­lu­tion funcvec-b

Ques­tion:

Graph­i­cally com­pare the spike di­a­gram of the 10-di­men­sion­al unit vec­tor ${\hat\imath}_3$, with com­po­nents (0,0,1,0,0,0,0,0,0,0), with the plot of the func­tion $f(x)$ $\vphantom0\raisebox{1.5pt}{$=$}$ 1. (No, they do not look alike.)

An­swer:

$$\begin{picture}(400,90)(-200,-20)\thinlines \put(-200,0){... ...){\line(1,0){110}} \put(-170,0){\vector(0,1){10}} \end{picture}$$

The equiv­a­lent of a unit vec­tor for func­tions is not the func­tion 1, it is the Dirac delta func­tion. This func­tion will be dis­cussed in de­tail later, but sim­ply put, it is a sin­gle, in­fi­nitely high spike.