7. Let
,
Then ,
Now ,
We know that by Cauchy-Schwarz inequality ,
This is the required relation .
7. (Norms of outer products) Find an expression relating the norm of the outer product |uv||...
Let V be a finite-dimensional inner product space. For an operator TEL(V), define its norm by ||T|:= max{||Tull VEV. ||0|| = 1}. (1) To explain this, note that {l|Tu ve V, || 0 || = 1} is a non-empty subset of [0,00). The expression max{||TV|| | V EV, ||0|| = 1} means the maximum, or largest, value in this set. In words, the norm of an operator describes the maximal amount that it 'stretches' (or shrinks) vectors. (a) (1 point)...
Please draw the major product or products of each of the following reactions. HBr/ UV light 5. Brz/ UV light 6. CI
7. Average age in a population. Suppose the 100-vector a represents the distribution of ages in a population, with xi being the number of i-1 year olds, for i = 1, . . . , 100. Find an expression for the average age across the population. (You can assume that xメ0) Your expression must use vector or matrix notation; you cannot use a sum over ages You can use any notation we've encountered, including vectors, matrices, matrix-vector products, inner product,...
Linear Algebra
2) General Inner Products, Length, Distance and Angle a) Determine if (u,v)-3uiv,-u,v, is a dot product b) Show that (u.v)-a+a,h,'2 is a product if a, 20 e)Let A-(41 ..)and B-G ) Use inner product on 4 -2 M (A, B aitai +apb +2a to find the length of A, B, namely ll-41 and 1 d) Find the angle between the two matrices above e) Find the distance between the two above matrices 0) For the functions (x)-1 and...
Find a minimal sum-of-products and product-of-sums expression for the function: f(A, B, C, D) = sigma m(1, 2, 3,5,13) + d (6,7,8,9,11)
Problem 1. Let the inner product (,) be defined by (u.v)xu (x)v (x) dx, and let the norm Iilbe defined by lIul-)Corhe target funtio), and work with the approximating space P4 Use Gram-Schmidt orthogonalization with this inner product to find orthogonal polynomials (x) through degree four. Standardize your polynomials such that p: (1) 1. (a) Form the five-by-five Gram matrix for this inner product with the basis functions p (x) degree 4 approximation o f (x) using the specified norm,...
1. (Difficulty: *) Write the value for the inner product (v(0), v(1)) where VO) and y(1) Enter answer here 2. (Difficulty: **) Consider the following vectors in R4 v (0) (1) and (2) = You can verify that the vectors are mutually orthogonal and have unit norm. How many different vectors v3) could we find such that {v(©), v(1), v(2), v(3)} is a full orthogonal basis in R4? 0 1 2 3 >3
ote: The norm of is denoted by |vand is calculated N a vector u Consider a subspace W of R4, W span(1, v2, v3, v4)). Where 0 из- 1. Find an orthonormal basis Qw of W and find the dimension of W 2. Find an orthonormal basis QWL of WL and find the dimension of WL 3. GIven a vector u- . find the Qw coordinate of Projw(v) . find the Qwa coordinate of Projwi (v) » find the coordinate...
A thick ring has inner radius 1/2R, outer radius R, and mass M. Find an expression for its rotational inertia. Express your answer in terms of the variables R and M.
pls answer 4,5,6 and 7
An) a) Find the magnitude of both vectors. b) Find dot product and cross product of both vectors c) Find the projection of w onto v 2) Let а:31 + 5, + 7k and b--6r +-10, + mk where m e R. a) Find the value for m such that vectors are orthogonal b) Find the value of m such that the cross product of the vectors is zero 3) a) Find the distance from...