Question

In: Advanced Math

show that for any two vectors u and v in an inner product space ||u+v||^2+||u-v||^2=2(||u||^2+||v||^2) give...

show that for any two vectors u and v in an inner product space

||u+v||^2+||u-v||^2=2(||u||^2+||v||^2)

give a geometric interpretation of this result fot he vector space R^2

Solutions

Expert Solution


Related Solutions

V is a subspace of inner-product space R3, generated by vector u =[1 1 2]T and...
V is a subspace of inner-product space R3, generated by vector u =[1 1 2]T and v =[ 2 2 3]T. T is transpose (1) Find its orthogonal complement space V┴ ; (2) Find the dimension of space W = V+ V┴; (3) Find the angle q between u and v; also the angle b between u and normalized x with respect to its 2-norm. (4) Considering v’ = av, a is a scaler, show the angle q’ between u...
(a).    Check <u,v> =2u1v1+3u2v2+u3v3 is inner product space or not. If yes assume u= (8,0,-8) &...
(a).    Check <u,v> =2u1v1+3u2v2+u3v3 is inner product space or not. If yes assume u= (8,0,-8) & v= (8,3,16) Find ||u|| ||v|| |<u, v>|2 Unit vector in direction of u and v Distance (u, v) Angle between u and v Orthogonal vectors of u and v. (b).    Show that <u,v> =u1v1-2u2v2+u3v3
Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ =...
Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ = 4, ∥u + v∥ = 5. Find the inner product 〈u, v〉. Suppose {a1, · · · ak} are orthonormal vectors in R m. Show that {a1, · · · ak} is a linearly independent set.
Suppose V is a finite dimensional inner product space. Prove that every orthogonal operator on V...
Suppose V is a finite dimensional inner product space. Prove that every orthogonal operator on V , i.e., <T(u),T(v)> = <u,v>, ∀u,v ∈ V , is an isomorphism.
Let U be a subset of a vector space V. Show that spanU is the intersection...
Let U be a subset of a vector space V. Show that spanU is the intersection of all the subspaces of V that contain U. What does this say if U=∅? Need proof
For the following exercises, use the vectors shown to sketch u + v, u − v, and 2u.
For the following exercises, use the vectors shown to sketch u + v, u − v, and 2u.
1. For this question, we define the following vectors: u = (1, 2), v = (−2,...
1. For this question, we define the following vectors: u = (1, 2), v = (−2, 3). (a) Sketch following vectors on the same set of axes. Make sure to label your axes with a scale. i. 2u ii. −v iii. u + 2v iv. A unit vector which is parallel to v (b) Let w be the vector satisfying u + v + w = 0 (0 is the zero vector). Draw a diagram showing the geometric relationship between...
For the following exercises, calculate u ⋅ v. Given the vectors shown in Figure 4, sketch u + v, u − v and 3v.
For the following exercises, calculate u ⋅ v.Given the vectors shown in Figure 4, sketch u + v, u − v and 3v.
2 Let u,v, and w be vectors, where u=(1,2,3,-1), v=(2,3,1,5) and w=(3,5,4,4). 2.1 Construct a basis...
2 Let u,v, and w be vectors, where u=(1,2,3,-1), v=(2,3,1,5) and w=(3,5,4,4). 2.1 Construct a basis for the vector space spanned by u, v and w. 2.2 Show that c=(1,3,2,1) is not in the vector space spanned by the above vectors u,v and w. 2.3 Show that d=(4,9,17,-11) is in the vector space spanned by the above vectors u,v and w, by expressing d as a linear combination of u,v and w.
Calculate the angle between the vectors u = {5, -2, 3} and v ={4,-5,7}
Calculate the angle between the vectors u = {5, -2, 3} and v ={4,-5,7}  give details.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT