Understanding Dot and Cross Product in Matrix Multiplication

Pippa
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Explain, for example, why you can cross three vectors (two at a time, following the usual rules), but not dot three vectors. Do you see the dot product "in action" in matrix multiplication? What sort of insights can the dot product give when trying to comprehend matrix multiplication?
 
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the dot product is a scalar, the cross product is still a vector
 
The dot product coincides with matrix multiplication , when your matrices are 1xn and
nx1.
 
Thanks Guys :D
 
np-
basically you get a number if its 1xn and nx1 and another vector if its nx1 and nx1
 
Yep, a scalar dotted with a vector is undefined. Finally, something I can answer! :-)
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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