MATH 1ZC3 Lecture 11: 5.1 Eigenvalue and Eigenvectors
20 Feb 2019
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31 3 1 a. x eigenate iittiona y everything to the right. Xi a i lookfora non trivialsolution tothisequator characteristice9hat t. fi egnmk. 0 iii f f r. ca ifa is intertable. It isnon innertable hasnontrialsolution so if ai a here a hi a i xi a mustbe noninnertable i detail a o. Sokeforx t t by lookingfornon o enget i solutionof xi a i o i i i de. Ii t ii infinitelymayotic gobefore i egienvector t14 110. I liftcivet 148k theni iscalleda libation of vt i. In pyoucantproduceanyofarectorfromanother indeed sumofconstant vector v corresponding toxandifevery i canbe. 2 if h v vnare writtenasalinearcombinationoftheset thentheset v vj vn iscalled. Tebasistigenspace correspondingtotheeigenvalex acollectionofalleigenvectorscorrespondto aspecific eigenvalue eg j f f"s i. I eg notindependent everyeigenvectoris amultipleofit everymultipleof is alinearcombination is a basisfortgenspae. I i l lo l i find andbasesfortheeigenspaces eg z matrixes in an egienspace z. I o 3 getegienialuesbywhytheequation defxl ako de i afo.
