show that a bounded Lineart on a complex Hilbert spase H is normal (i-eTT* = T*T) if and only if 11+ * (~)||-||+(x) || for all xeH-using That for a normal operator ||7²|1=117|1² this to show

Q: what are domine, Vange and null space o F Tisra-s Ty Rom R?into Re 1

A: The given functions are                                 T1:ℝ2→ℝ2 such that T1ξ1,ξ2=ξ1,0.T2:ℝ2→ℝ2…

Q: Which of the following monic quadratic polynomials is irreducible in ℤ_3[x]? Hint: f(x)=(x-a)(x-b)…

A:

Q: How many injective functions have domain {a,b,c} and codomain [100]?

A:

Q: prove for all x,y in R^n: (1+||x+y||) ≥(1+||x||)/(1+||y||)

A: Sol:- The inequality to be proven is: (1 + ||x + y||) ≥ (1 + ||x||)/(1 + ||y||) Let's start by…

Q: 2. (a) Let A = {x = [0, 1]: x has a decimal representation not containing the digit 5.} Show that A…

A: We shall use certain results from measure theory

Q: to Prove that : Ge = { in (+ + ² ) Z tan z =

A:

Q: The product of sum (max term) form of the boolean function F = x +y'z is

A:

Q: Let & € N. Prove by using the contra-positive that if ³ is odd then is odd. Proof: Choose which of…

A: Introduction: The basis for proof by contra positive is the idea that an implication equals its…

Q: Linear Algebra: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2. Is {p1,p2,p3} a…

A: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2.

Q: prove that the covariant derivate satisfies leibniz's rule

A: The main reason behind the covariant derivative satisfying Leibniz's rule is it maintains chain rule…

Q: Please help me with this question. I am having trouble understanding what to do. Please show all…

A: The objective of the first part of the question is to prove that the sum of two functions, f1 and…

Q: For all a, b in R, show that -max{a^2, b^2} <ab max{a^2, b^2}.

A: To prove that for all (a,b)in(R), [max(−a2b2,ab)≤ab≤max(a2b2)] We'll consider three cases: 1.…

Q: Prove that if AERnxm then rank(A) = rank(AT)

A: If A ∈ Rnxm then we have to prove that rank(A) = rank(AT)

Q: Find oxthogonal uncdary diagonalizing an or matri'y to lMowing tor One 2 (a) (b) 3 -2 -2

A: A square matrix A is called as orthogonal matrix if AxAT=ATxA=I where AT transpose of matrix A. and…

Q: Since P+ Q, it follows that [(a1 + a3 + a5) – (a2 + a4)] [(B1 + B3 + B5) + A (82 + B4)]' | P+Q =…

A:

Q: f for ƒ : R - {2} → R- { 5} indicated by f (x) =(5x +1)/(x -2a), a bijection can be made from [0, 1)…

A: Bijective function: The domain is set A and the co-domain in set B relates elements of two sets A…

Q: metoix space and d[211?(₂) for all ₁2 ER 2,12₂ 17. (*/ 1²(₂) d is matrie X. let (Xid) be d' XXR…

A:

Q: Please help me with this question. I am having trouble understanding what to do. Please show all…

A: The objective of the first part of the question is to prove that the sum of two functions, f1 and…

Q: 1 Let {f} be a sequence of real nonnegative functions on R', and consider the following four state…

A: (1) Given that fn is a sequence of real non negative functions. (a) If f1 and f2 are upper semi…

Q: Let A ∈ (R) be given If A is nonsingular, prove that adj(A) is nonsingular and adj(A)^-1 = (A^-1)

A:

Q: FX)= (x-4)²

A: Note: - “Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: (b) Find an expression az + ba? + ca +d so that this new polynomial is orthogonal to all the…

A: Solution of part (b): The inner product on continuous functions on -2,2 is defined by…

Q: Let a in F_p, a is non zero then show

A:

Q: - Give on homeomorphism./ example of continous function fiR-3R which is not o .//

A:

Q: Let such that 1 0 1 -1 2 -6⠀⠀⠀-0-0 1 1 3 -1 b 000 0 Then there exist scalars b A True False = X1,…

A:

Q: If l is a line through (0,0), the point (0,0) divides the line l into two rays. Also, a…

A: To determine for which rays starting at the origin ez is bounded, we need to analyze the behavior of…

Q: 25. Find Uge B and Be B for each collection B. BE 4 (a) + *+{[11] N}*(0) + {[L1 =): N} N}₁ B+ :n (c)…

A:

Q: Let f: A→ B, where A= {1,-1}, B= {1,2,3}, and f(x)= 3×x²+2, find Range إجابتك * Codomain إجابك * Is…

A:

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…

Q: The logistic function given by f (x) = is a sigmoid (s-shaped) function useful in many 1+e-* areas…

A: (a) Given that a logistic function fx is defined as: fx=11+e-x which is a sigmoid function and given…

Q: Let a ∈ G be such that |a| = ∞ . For m≠n prove that a^m ≠a^n

A:

Q: (b) Let # ACR be bounded below. Prove that Inf (A) =-Sup(-A). %3D

A: Let A is non-empty subset of real number . Let A be bounded below then we have to show that  Inf(A)…

Q: Determine the quadature rule of the form | f(r) dr = Aof(ro) + A1f(£1) + - *·+ Anf(Tn) a. when the…

A: