How to Find the Adjoint (Adjugate) of a Matrix
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YouTubeGreeneMath.com
How to Find the Adjoint (Adjugate) of a Matrix
http://www.greenemath.com/ http://www.facebook.com/mathematicsbyjgreene In this lesson, we will learn how to find the classical adjoint (which is also known as an adjugate) of a matrix. The adjoint of a matrix is found using two steps. The first step is to create a matrix of cofactors. A cofactor for a given entry is found by multiplying (-1 ...
已浏览 8万 次2020年3月16日
Self-adjoint Operator Examples
Adjoint Operator (20 points) Derive the following properties of the adjoint of an operator:
Adjoint Operator (20 points) Derive the following properties of the adjoint of an operator:
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SOLVED: For the very special case λ=0 and q(x)=0, the self-adjoint eigenvalue equation becomes (d)/(d x)[p(x) (d u(x))/(d x)]=0 satisfied by (d u)/(d x)=(1)/(p(x)) Use this to obtain a "second" solution of the following: (a) Legendre's equation; (b) Laguerre's equation; and (c) Hermite's equation. ANS. (a) u2(x)=(1)/(2)ln(1 x)/(1-x) (b) u2(x)-u2(x0)=∫x0^x e^t(d t)/(t) ; (c) u2(x)=∫0^x e^t^2 d t These second solutions illustrate the divergent behavior usually found in a second sol
SOLVED: For the very special case λ=0 and q(x)=0, the self-adjoint eigenvalue equation becomes (d)/(d x)[p(x) (d u(x))/(d x)]=0 satisfied by (d u)/(d x)=(1)/(p(x)) Use this to obtain a "second" solution of the following: (a) Legendre's equation; (b) Laguerre's equation; and (c) Hermite's equation. ANS. (a) u2(x)=(1)/(2)ln(1 x)/(1-x) (b) u2(x)-u2(x0)=∫x0^x e^t(d t)/(t) ; (c) u2(x)=∫0^x e^t^2 d t These second solutions illustrate the divergent behavior usually found in a second sol
numerade.com
2021年6月7日
CODEX ALPHA: Annals Submission Draft Abstract We present a spectral resolution of the Riemann Hypothesis via the Omega Operator, a compact self-adjoint operator on a weighted s²-space over primes. The eigenvalues of this operator match the nontrivial zeros of the Riemann zeta function ξ(1/2 is), verified through Fredholm determinant analysis and prime-zero duality theorems. A complete trace formula demonstrates analytic continuation and functional symmetry Z(s) = Z(1 - s), with all zeros align
3:02
CODEX ALPHA: Annals Submission Draft Abstract We present a spectral resolution of the Riemann Hypothesis via the Omega Operator, a compact self-adjoint operator on a weighted s²-space over primes. The eigenvalues of this operator match the nontrivial zeros of the Riemann zeta function ξ(1/2 is), verified through Fredholm determinant analysis and prime-zero duality theorems. A complete trace formula demonstrates analytic continuation and functional symmetry Z(s) = Z(1 - s), with all zeros align
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