Textbook Guide Mathematics: Quadratic Equation, Triangular Matrix, Invertible Matrix

244 views21 pages
1 Dec 2016
School
Department
Course
Professor

Document Summary

This number obtained from utv is known as the inner product of u and v and is often written as u. v and sometimes referred to as dot product. If, (cid:1873)= [ (cid:1873)(cid:2869)(cid:1873)(cid:2870)(cid:1873)(cid:2871)(cid:1709)(cid:1873)(cid:3041)] (cid:1853)(cid:1866)(cid:1856) (cid:1874)= [ (cid:1874)(cid:2869)(cid:1874)(cid:2870)(cid:1874)(cid:2871)(cid:1709)(cid:1874)(cid:3041)] then the inner product of u and v is: [(cid:1873)(cid:2869) (cid:1873)(cid:2870) (cid:1873)(cid:2871) (cid:1710) (cid:1873)(cid:3041)][ (cid:1874)(cid:2869)(cid:1874)(cid:2870)(cid:1874)(cid:2871)(cid:1709)(cid:1874)(cid:3041)] =(cid:1873)(cid:2869)(cid:1874)(cid:2869)+ (cid:1873)(cid:2870)(cid:1874)(cid:2870)+ (cid:1873)(cid:2871)(cid:1874)(cid:2871)+ (cid:1710)+ (cid:1873)(cid:3041)(cid:1874)(cid:3041) Considering vectors u, v and w present in rn with c being a scalar quantity, (cid:1853). (cid:2203). (cid:2204)=(cid:2204). (cid:2203) (cid:1854). (cid:4666)(cid:2203)+(cid:2204)(cid:4667). (cid:2205)=(cid:2203). (cid:2205)+(cid:2204). (cid:2205) (cid:1855). (cid:4666)(cid:1855)(cid:2203)(cid:4667). (cid:2204)=(cid:1855)(cid:4666)(cid:2203). (cid:2204)(cid:4667)=(cid:2203). (cid:4666)(cid:1855)(cid:2204)(cid:4667) (cid:1856). (cid:2203). (cid:2203)(cid:3410)(cid:2777) (cid:1853)(cid:1866)(cid:1856) (cid:2203). (cid:2203)=(cid:2777) (cid:1861)(cid:1858) (cid:1853)(cid:1866)(cid:1856) (cid:1867)(cid:1866)(cid:1864) (cid:1861)(cid:1858) (cid:2203)=(cid:2777) From the above given properties, it can be further proved that, (cid:4666)(cid:1855)(cid:2869)(cid:2203)(cid:2778)+(cid:1855)(cid:2870)(cid:2203)(cid:2870)+(cid:1710)+(cid:1855)(cid:2203)(cid:4667). (cid:2205)= (cid:1855)(cid:2869)(cid:4666)(cid:2203)(cid:2778). (cid:2205)(cid:4667)+ (cid:1710)+(cid:1855)(cid:4666)(cid:2203)(cid:2193). (cid:2205)(cid:4667) For any v belonging to rn with quantities v1, v2, vn the length is a non-negative scalar quantity v defined as; Also, for any scalar quantity c, the length of cv is c times the length of v, i. e. (cid:1855)(cid:1822) =|(cid:1855)| (cid:1822) .

Get access

Grade+20% off
$8 USD/m$10 USD/m
Billed $96 USD annually
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
40 Verified Answers

Related Documents

Related Questions