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anti Symmetric electromagne the tensor Components IF te fu is an 1 Ereld tensor Show that...
Ģ) 1. Given the components of a tensor Λ1a as the matrix (0 1 0 1...
Ģ) 1. Given the components of a tensor Λ1a as the matrix (0 1 0 1 -1 0 2 2 0 01 102 0, find a) The components of the symmetric tensor M(a3) and the antisymme tric tensor ΛΊαβ. b) the components of M and M%
1. Show that for a lossless N-port network, REAL([Z]) = -REAL([Z]T).(The real matrix is anti-symmetric)
1. Show that for a lossless N-port network, REAL([Z]) = -REAL([Z]T).(The real matrix is anti-symmetric)
R3. Problem 4. (3+2+3 pts) Consider an arbitrary skew-symmetric tensor 22: R3 (i) Show that I...
R3. Problem 4. (3+2+3 pts) Consider an arbitrary skew-symmetric tensor 22: R3 (i) Show that I be represented by a vector w as follows: VE R3 Ωυ =ωXυ. (ii) Next, show that cofactor of 12 equals wow. (iii) Prove that 1+1 is always invertible.
1. a) What is the fundamental difference between symmetric and anti-symmetric matrix? b) Given th...
1. a) What is the fundamental difference between symmetric and anti-symmetric matrix? b) Given the laminate shown below compute A2, Bn, and Dis. Given that E, 155 GPa; Ep 12.1 GPa; V12-0.248; G12-4.4 GPa. Z3-15 0-30° -5 0-90 0-0° z1-5 mm All dimensions are in Zo-15
1. a) What is the fundamental difference between symmetric and anti-symmetric matrix? b) Given the laminate shown below compute A2, Bn, and Dis. Given that E, 155 GPa; Ep 12.1 GPa; V12-0.248; G12-4.4 GPa....
1. Consider the conjugate-metric tensor, whose components in inertial system S is element of the matrix...
1. Consider the conjugate-metric tensor, whose components in inertial system S is element of the matrix y = diag(-1, +1, +1, +1). In another inertial system s', the components of the conjugate- metric tensor are given by = AA, where A', is element to of the matrix A= - n | - n1+ 6 -1) 1 - ny 7:6-1) -yon. 7:7(7-1) - ny (7-1) 1+n: 6-1) 7.7, 6-1) 1.6 - 1) 6-1) 1+ (-1) ) that is associated with the...
Spherical tensor operators Given: Az = ¿ bemPem(s) (1) m =-l Where Tem are the tesseral...
Spherical tensor operators
Given: Az = ¿ bemPem(s) (1) m =-l Where Tem are the tesseral combinations of the spherical-tensor operators Tem: 1) Tem() + Te,-m(S)] Te-m(s) = šal(+1)m+Tem(5) + Te-m(s)] Show that for f = 1, eq. (1) becomes: în = b1,1Şx + b1,-1Ŝy + b1,0Ŝz Where Ŝx, Ŝy, Ŝy are the spin-operators
How many anti-symmetric relations on the set A = {1, 2, 3, 4, 5, 6} contain...
How many anti-symmetric relations on the set A = {1, 2, 3, 4, 5, 6} contain the ordered pairs (2, 2), (3, 4) and (5, 6)?
A square matrix E∈Mn×n(R) is idempotent if E2=E. It is symmetric if E = tE. (a) Let V⊆Rn be a subspace of Rn, and consider the orthogonal projection projV:Rn→Rn onto V. Show that the representing matr...
A square matrix E∈Mn×n(R) is idempotent if E2=E. It is symmetric if E = tE. (a) Let V⊆Rn be a subspace of Rn, and consider the orthogonal projection projV:Rn→Rn onto V. Show that the representing matrix E = [projV]EE of proj V relative to the standard basis E of Rn is both idempotent and symmetric. (b) Let E∈Mn×n(R) be a matrix that is both idempotent and symmetric. Show that there is a subspace V⊆Rn such that E= [projV]EE. [Hint: What...
1. a) b) QUESTION 1 In coordinate system S, the components of a covariant tensor of...
1.
a)
b)
QUESTION 1 In coordinate system S, the components of a covariant tensor of order 2 take the following values at a certain point P: T.1 = 3, T21 = -5, T12 = -5, T22 = 7 Find component 722 in coordinate system Š obtained by the coordinate transformation: x = x and 32- with A = -6 and B = 1 QUESTION 2 Find the correct transformation formula. (Note that the summation symbol 2 is omitted everywhere...
1. Suppose that A is a symmetric matrix with A A+ orome integer 1. Show that...
1. Suppose that A is a symmetric matrix with A A+ orome integer 1. Show that A is k+1 idempotent
Ģ) 1. Given the components of a tensor Λ1a as the matrix (0 1 0 1 -1 0 2 2 0 01 102 0, find a) The components of the symmetric tensor M(a3) and the antisymme tric tensor ΛΊαβ. b) the components of M and M%
R3. Problem 4. (3+2+3 pts) Consider an arbitrary skew-symmetric tensor 22: R3 (i) Show that I be represented by a vector w as follows: VE R3 Ωυ =ωXυ. (ii) Next, show that cofactor of 12 equals wow. (iii) Prove that 1+1 is always invertible.
1. a) What is the fundamental difference between symmetric and anti-symmetric matrix? b) Given the laminate shown below compute A2, Bn, and Dis. Given that E, 155 GPa; Ep 12.1 GPa; V12-0.248; G12-4.4 GPa. Z3-15 0-30° -5 0-90 0-0° z1-5 mm All dimensions are in Zo-15
1. a) What is the fundamental difference between symmetric and anti-symmetric matrix? b) Given the laminate shown below compute A2, Bn, and Dis. Given that E, 155 GPa; Ep 12.1 GPa; V12-0.248; G12-4.4 GPa....
1. Consider the conjugate-metric tensor, whose components in inertial system S is element of the matrix y = diag(-1, +1, +1, +1). In another inertial system s', the components of the conjugate- metric tensor are given by = AA, where A', is element to of the matrix A= - n | - n1+ 6 -1) 1 - ny 7:6-1) -yon. 7:7(7-1) - ny (7-1) 1+n: 6-1) 7.7, 6-1) 1.6 - 1) 6-1) 1+ (-1) ) that is associated with the...
Spherical tensor operators
Given: Az = ¿ bemPem(s) (1) m =-l Where Tem are the tesseral combinations of the spherical-tensor operators Tem: 1) Tem() + Te,-m(S)] Te-m(s) = šal(+1)m+Tem(5) + Te-m(s)] Show that for f = 1, eq. (1) becomes: în = b1,1Şx + b1,-1Ŝy + b1,0Ŝz Where Ŝx, Ŝy, Ŝy are the spin-operators
1.
a)
b)
QUESTION 1 In coordinate system S, the components of a covariant tensor of order 2 take the following values at a certain point P: T.1 = 3, T21 = -5, T12 = -5, T22 = 7 Find component 722 in coordinate system Š obtained by the coordinate transformation: x = x and 32- with A = -6 and B = 1 QUESTION 2 Find the correct transformation formula. (Note that the summation symbol 2 is omitted everywhere...
1. Suppose that A is a symmetric matrix with A A+ orome integer 1. Show that A is k+1 idempotent
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