Managing Intents for Android Apps
"Learn how to bind application components, navigate between screens, start new activities explicitly or implicitly, and use intent filters to service implicit intents in Android development. Understand the concepts of explicit and implicit intents, intent resolution, and native Android actions such as ACTION_VIEW and ACTION_CALL."
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Presentation Transcript
The Dot product A.G.Farhan . . .
#Let u=(u1, u2,, un), be a vector in a vector space V. The length (norm or magnitude ) of u is #The dot product of u=(u1, ,un) and v=(v1, ,vn) is written u.v and is defined two ways: 1. u.v= u1v1+u2v2+ +unvn 2. u.v= |u||v|cos , where is the angle formed by u and v. Example: Find u.v , where u =(3, 4,1) and v = (5,2, 6), then find the angle a formed by u and v.
Solution: Using the first method of calculation, we have u.v= (3)(5)+(-4)(2)+(1)(-6)= =15-8-6=1 To find , we use the second method
Some Properties of the Dot Product 1) u.v=v.u 4) u.(v+w)=u.v+u.w 5) If u v > 0 then the angle formed by the vectors 6 6) ) If u If u v v < 0 0 then the angle formed by the vectors then the angle formed by the vectors 7) If u v = 0, then the angle formed by the vectors is
DEFINITION Let u and v are vectors in a vector space V. if u.v=0, then we say that u and v are orthogonal. DEFINITION Let V. if =0 for all i then we say that S form an orthogonal set. In additional if all the vectors of an orthogonal set S has length ,then S is called an orthonormal set. THEOREM Any orthogonal set is linearly independent.
Gram-Schmidt process: If is a basis for a vector space V. then we Can define an orthogonal basis for V by using the following steps:
EXAMPLE Let be a basis for . We will use Gram-Schmidt process to find orthogonal and orthonormal bases for . =(1,1,0)
is an orthogonal basis for Since then the set is an orthonormal basis for
