what-is-the-intutive-understanding-of-eigenvalues-and-vectors-with-practical-examples-

Question Number 5859 by wanderer last updated on 02/Jun/16

w h a t i s t h e i n t u t i v e u n d e r s t a n d i n g o f

e i g e n v a l u e s a n d v e c t o r s . w i t h p r a c t i c a l

e x a m p l e s .

Commented by FilupSmith last updated on 02/Jun/16

A vector is a direction and magnitude .

Lets say you face North .

if a = [\begin{matrix} 1 \\ 0 \end{matrix}], a \in R^{2}

this can be interperated as 1 unit to the

right .

Application in Physics include, for example

projectile motion, velocity, forces, etc .

For example :

F = m a

F and a are vectors .

So therefore the Force has the same

direction as a but a different value / magnitued

due to being multiplied by m .

e . g .

a = 4 m / s^{2} downwards

m = 2 kg

∴ F = (4 \times 2) Newtons downwards

F = 8 N downwards