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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 Av=𝛌v
$$\mathrm{can}\:\mathrm{you}\:\mathrm{guy}\:\mathrm{explian}\:\mathrm{why} \\ $$$$\mathrm{we}\:\mathrm{need}\:\mathrm{a}\:\mathrm{eighgen}\:\mathrm{value}\:\mathrm{eighgen}\:\mathrm{vector} \\ $$$$\mathrm{and}\:\mathrm{mean}?? \\ $$$$\mathrm{such}\:\mathrm{as}\:\mathrm{A}\boldsymbol{\mathrm{v}}=\boldsymbol{\lambda\mathrm{v}} \\ $$$$ \\ $$
Commented by mr W last updated on 07/Apr/24
the question is too general to answer.  just like why we need calcules and  what it means.  for such general questions it′s better  when you consult google or the like.
$${the}\:{question}\:{is}\:{too}\:{general}\:{to}\:{answer}. \\ $$$${just}\:{like}\:{why}\:{we}\:{need}\:{calcules}\:{and} \\ $$$${what}\:{it}\:{means}. \\ $$$${for}\:{such}\:{general}\:{questions}\:{it}'{s}\:{better} \\ $$$${when}\:{you}\:{consult}\:{google}\:{or}\:{the}\:{like}. \\ $$
Commented by MaruMaru last updated on 07/Apr/24
mmmm.....ok..... :(
$$\mathrm{mmmm}…..{o}\mathrm{k}…..\::\left(\right. \\ $$
Commented by A5T last updated on 07/Apr/24
Generally, an eigenvector is a vector,say A, whose  transformation of another vector,say v, only  results in the “stretching” of v. That is,no change  in direction but only change in magnitude.  So, the equation that represents this is  Av=λv; where λ is a scalar.
$${Generally},\:{an}\:{eigenvector}\:{is}\:{a}\:{vector},{say}\:\boldsymbol{\mathrm{A}},\:{whose} \\ $$$${transformation}\:{of}\:{another}\:{vector},{say}\:\boldsymbol{\mathrm{v}},\:{only} \\ $$$${results}\:{in}\:{the}\:“{stretching}''\:{of}\:\boldsymbol{\mathrm{v}}.\:{That}\:{is},{no}\:{change} \\ $$$${in}\:{direction}\:{but}\:{only}\:{change}\:{in}\:{magnitude}. \\ $$$${So},\:{the}\:{equation}\:{that}\:{represents}\:{this}\:{is} \\ $$$$\boldsymbol{{A}\mathrm{v}}=\lambda\boldsymbol{\mathrm{v}};\:{where}\:\lambda\:{is}\:{a}\:{scalar}. \\ $$
Commented by MaruMaru last updated on 07/Apr/24
thx :)
$$\left.{thx}\::\right) \\ $$

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