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Linear Algebra
Let C=[4,0,-2 2,5,4 0,0,5]
Diagonalise matrix C, if possible.
Diagonalise matrix C, if possible.
Linear Algebra
Find a system of linear equations Ax = b for which there are multiple minimum one-norm solutions.
Linear Algebra
Please show that, if x is a cluster point of {x^k}, and if d(x,x^k) >= d(x,x^(k+1)), for all k, then x is the limit of the sequence.
Linear Algebra
Please show that, if {s^k} is bounded, then, for any element c in the metric space, there is a constant t>0 with d(c,s^k)<=t, for all k.
Linear Algebra
Please show that any convergent sequence in a metric space is bounded, then find a bounded sequence of real numbers that is not convergent.
Linear Algebra
how i find rank and nulity and rank space of linear transformatin
Linear Algebra
****comma indicates a new row****
Show that the 2x2 matrix S = [0 1, -1 0] is real, normal, and has eigenvalues +-i. Show that the eigenvalues of N^TN are both one. (where T is transpose).
Show that the 2x2 matrix S = [0 1, -1 0] is real, normal, and has eigenvalues +-i. Show that the eigenvalues of N^TN are both one. (where T is transpose).
Linear Algebra
k is an eigenvalue of S iff det(S-kI) = 0, and det(AB) = det(A)det(B).
Please use these facts to show that k^2 is an eigenvalue of S^2 iff either k or -k is an eigenvalue of S. Then use this result to show that p(S)^2 = p(S^2).
Please use these facts to show that k^2 is an eigenvalue of S^2 iff either k or -k is an eigenvalue of S. Then use this result to show that p(S)^2 = p(S^2).
Linear Algebra
k is an eigenvalue of S iff det(S-kI) = 0, and det(AB) = det(A)det(B).
Use these facts to show that k^2 is an eigenvalue of S^2 iff either k or -k is an eigenvalue of S. Then use this result to show that p(S)^2 = p(S^2).
Use these facts to show that k^2 is an eigenvalue of S^2 iff either k or -k is an eigenvalue of S. Then use this result to show that p(S)^2 = p(S^2).
Linear Algebra
Let * equal conjugate transpose.
Given a Hermitian Matrix H, show that the eigenvalues of said matrix are real by computing the conjugate transpose of the 1 by 1 matrix z*Hz.
Given a Hermitian Matrix H, show that the eigenvalues of said matrix are real by computing the conjugate transpose of the 1 by 1 matrix z*Hz.
