MATH 307 Lecture Notes - Lecture 15: Invertible Matrix
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Forany u v wev i utv e u. Iv there exists8 in v s 1 uto u ut l u i v thereexists u eu s t. Forscalars a b e f scalarset vi a u ev. 3 thesetof all mxn matrices theaddition of two mxn matrices is over well defined. 4 thesetofall symmetric nxn matrices it a bev checka1bev. At a b1 13 a113it at113t atb v i a 113 isalsosymmetric i. e atbev. 5 theset of allfunctions on a b f g ftg x dt x fix 1g x dfx. Thesetofallcontinuousfunctions on a b some examplesthatare notvectorspaces subsetof15. V l0 i l ev hi 2 v. Det asubsets et v is a subspaceetu it for all u ves and allscalars a bef i ii. V thesetofall nxn matrices 5 thesetof all symmetric n xn mathies i s is a subspaceof v.
