Question Number 206107 by MaruMaru last updated on 07/Apr/24
$$\mathrm{can}\:\mathrm{you}\:\mathrm{guy}\:\mathrm{explian}\:\mathrm{why} \\ $$$$\mathrm{we}\:\mathrm{need}\:\mathrm{a}\:\mathrm{eighgen}\:\mathrm{value}\:\mathrm{eighgen}\:\mathrm{vector} \\ $$$$\mathrm{and}\:\mathrm{mean}?? \\ $$$$\mathrm{such}\:\mathrm{as}\:\mathrm{A}\boldsymbol{\mathrm{v}}=\boldsymbol{\lambda\mathrm{v}} \\ $$$$ \\ $$
Commented by mr W last updated on 07/Apr/24
$${the}\:{question}\:{is}\:{too}\:{general}\:{to}\:{answer}. \\ $$$${just}\:{like}\:{why}\:{we}\:{need}\:{calcules}\:{and} \\ $$$${what}\:{it}\:{means}. \\ $$$${for}\:{such}\:{general}\:{questions}\:{it}'{s}\:{better} \\ $$$${when}\:{you}\:{consult}\:{google}\:{or}\:{the}\:{like}. \\ $$
Commented by MaruMaru last updated on 07/Apr/24
$$\mathrm{mmmm}…..{o}\mathrm{k}…..\::\left(\right. \\ $$
Commented by A5T last updated on 07/Apr/24
$${Generally},\:{an}\:{eigenvector}\:{is}\:{a}\:{vector},{say}\:\boldsymbol{\mathrm{A}},\:{whose} \\ $$$${transformation}\:{of}\:{another}\:{vector},{say}\:\boldsymbol{\mathrm{v}},\:{only} \\ $$$${results}\:{in}\:{the}\:“{stretching}''\:{of}\:\boldsymbol{\mathrm{v}}.\:{That}\:{is},{no}\:{change} \\ $$$${in}\:{direction}\:{but}\:{only}\:{change}\:{in}\:{magnitude}. \\ $$$${So},\:{the}\:{equation}\:{that}\:{represents}\:{this}\:{is} \\ $$$$\boldsymbol{{A}\mathrm{v}}=\lambda\boldsymbol{\mathrm{v}};\:{where}\:\lambda\:{is}\:{a}\:{scalar}. \\ $$
Commented by MaruMaru last updated on 07/Apr/24
$$\left.{thx}\::\right) \\ $$