can you guy explian why we need a eighgen value eighgen vector and mean?? such as Av=𝛌v


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Question Number 206107 by MaruMaru last updated on 07/Apr/24

$can you guy explian why$ $we need a eighgen value eighgen vector$ $and mean ? ?$ $such as A v = λ v$
Commented by mr W last updated on 07/Apr/24

$t h e q u e s t i o n i s t o o g e n e r a l t o a n s w e r .$ $j u s t l i k e w h y w e n e e d c a l c u l e s a n d$ $w h a t i t m e a n s .$ $f o r s u c h g e n e r a l q u e s t i o n s {i t}^{'} s b e t t e r$ $w h e n y o u c o n s u l t g o o g l e o r t h e l i k e .$
Commented by MaruMaru last updated on 07/Apr/24

$mmmm . . . . . o k . . . . . : ($
Commented by A5T last updated on 07/Apr/24

$G e n e r a l l y, a n e i g e n v e c t o r i s a v e c t o r, s a y A, w h o s e$ $t r a n s f o r m a t i o n o f a n o t h e r v e c t o r, s a y v, o n l y$ $r e s u l t s i n t h e ‘ ‘ {s t r e t c h i n g}^{″} o f v . T h a t i s, n o c h a n g e$ $i n d i r e c t i o n b u t o n l y c h a n g e i n m a g n i t u d e .$ $S o, t h e e q u a t i o n t h a t r e p r e s e n t s t h i s i s$ $A v = λ v; w h e r e λ i s a s c a l a r .$
Commented by MaruMaru last updated on 07/Apr/24

$t h x :)$
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