Let H be a hermitian matrix, i.e. H = H*. Now U := eiH is a unitary matrix. Let H = († 8). aER, beC with b + 0. (i) Calculate eiH using the normalized eigenvectors of H to construct a unitary matrix V such that V*HV is a diagonal matrix. (ii) Specify a, b such that we find the unitary matrix 0 U = (1₂8).

Q: 10. It is known that matrix A 4x4 has the following eigenvalues: 2, =-2, 2, = 1, z =-1, 24 = 2.…

A:

Q: Let {v₁,...Vn} R" be linearly independnt. (a) Let A be a singular n × n matrix. Prove or disprove…

A: Let a set of vectors be For m scalars  satisfyIf the only solution is Then the vectors  are linearly…

Q: A 3 by 3 matrix B is known to have eigenvalues -1, 2, 3. This information is enough to find: (a) the…

A:

Q: Let A = Diagonalise this matrix. That is, find a diagonal matrix D and an invertible matrix Q such…

A:

Q: symmetric matrix and A1 and alues of the matrix. The 2 1 gen vector is 2 and 1

A:

Q: Consider the sequence {ax}, defined by а, 3D 1, ад — 1, and ak 3 а-1+ ak-2 for k > 3. Compute as.

A: We have given two terms of sequence {a_k}, a_1=1 and a_2=1 and then sequence {a_k} is defined by…

Q: 3 Determine all eigenspaces for the matrix A

A: Given: To Find All eigenspaces of the given matrix.   Eigen Space:

Q: (31/1/2 03 A= 1 1 - 1 3 3 3 1 0 0 0 0 0 0 0 -130 0 0 10 3/

A: According to the given matrix A, find an invertible matrix P such that .

Q: ume equals 2.74 million in 2015 and 4.19 million in 20 2015, then t5 for 2020. Expressing the two…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Suppose A is an n by n invertible matrix. Then A O True O False Suppose A and Bare n by n invertible…

A:

Q: Let -3 4 A-[ 3³ -1], E-[42], F-[^2} = = = -5 Compute the indicated matrix. (If this is not possible,…

A:

Q: let A nonsingular matrix, c #0, c scalar (cA)" = CA -1 -1 %3D Select one: True O False

A:

Q: Let A = [aij] given by a x bij = (i-j)^3 is a: * Anti-Symmetric matrix Symmetric matrix Identity…

A:

Q: Show that if annxn matrix U satisfies (Ux)· (Uy) = x•y for all x and y in Rn, then U is an…

A:

Q: Suppose A is a symmetric matrix. (Au)" : u"A

A:

Q: If Aand B are invertible matrices of the same order, Then show that AB is invertible matrices.…

A: LHS   =  (AB)-1  RHS  =  B-1A-1 For    (AB)-1  =  B-1A-1 ,   RHS * inverse of LHS = i…

Q: 3х3 real inant of

A:

Q: Let A be an orthogonal matrix. Show that cA is orthogo- nal if and only if c = ±1.

A: Given:            A be an orthogonal matrix.

Q: Let A be a square, invertible matrix and let A' be its transpose. Which of the following statements…

A: Solution

Q: Prove det(A) = det(A'), for an upper triangular matrix A.

A:

Q: -2 3.

A:

Q: Choose the 2 by 2 nondiagonal matrix such that its eigenvalues are different positive numbers…

A: We first write a 2×2 non diagonal matrix whose eigen values are different positive numbers then we…

Q: Find an invertible matrix P that diagonalizes the matrix A = (12) i.e. , a matrix P such that P-AP…

A:

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: Matrix A (image) has the following set of eigenvectors: x1 = (1, 0,1), x2 = (0,1,0), and x3 = (-1,…

A: A matrix is a mathematical object containing numbers arranged in rows and columns. If the matrix…

Q: y 13. T y | B1 %3D B2: %3D 1

A:

Q: Write down a n × n matrix A such that Cond(A) =1, but determinant(A) → 0 as n → ∞.

A: claim- write down a n×n matrix A such that CondA=1, but detA→0 as n→∞. it is known that condition…