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This is my version of explanation. I would suggest you to come up with your own explanation. The best way would be for you to try explain this to somebody else in your own words.

Following is my version of explanation, but this is just an example. You may come up with a better version.

Inner Prdouct - Vector

t = linspace(0,2*pi,80);

nt = [0 1/4*pi 2/4*pi 3/4*pi 4/4*pi 5/4*pi 6/4*pi 7/4*pi 8/4*pi];

hFig = figure(1,'Position',[300 300 400 300]);

subplot(2,3,[1 2 3]);

hold on;

plot(t,sin(t),'r-');

plot(nt,sin(nt),'ro','MarkerFaceColor',[1 0 0],'MarkerSize',7);

xlim([0 2*pi]);

ylim([-1 1]);

set(gca,'xtick',[0 0.25*pi 0.5*pi 0.75*pi pi 1.25*pi 1.5*pi 1.75*pi 2.0*pi]);

set(gca,'xticklabel',{'0','1 pi/4','2 pi/4','3 pi/4','4 pi/4','5 pi/4','6 pi/4','7 pi/4','8 pi/4'});

grid on;

hold off;

n = 2.0;

subplot(2,3,[4 5 6]);

hold on;

plot(t,sin(n * t),'b-')

plot(nt,sin(n * nt),'bo','MarkerFaceColor',[0 0 1],'MarkerSize',7);

xlim([0 2*pi]);

ylim([-1 1]);

set(gca,'xtick',[0 0.25*pi 0.5*pi 0.75*pi pi 1.25*pi 1.5*pi 1.75*pi 2.0*pi]);

set(gca,'xticklabel',{'0','1 pi/4','2 pi/4','3 pi/4','4 pi/4','5 pi/4','6 pi/4','7 pi/4','8 pi/4'});

grid on;

hold off;

v1 = sin(nt);

v2 = sin(n * nt)

v1 * v2'