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- We can use the spectral representation to solve a system of linear homogeneous ordinary not all zero such that the linear combination ...11 KB (1,774 words) - 15:02, 13 September 2010
- [[Category:Linear operators]] ...3 KB (439 words) - 07:52, 4 June 2008
- 2 KB (253 words) - 07:53, 4 June 2008
- Linear operators can be thought of as infinite dimensional matrices. Hence we can use well known results from matrix theory when dealing with linear operators. ...10 KB (1,661 words) - 19:04, 24 February 2025
- if <math>\mathbf{x} = \mathbf{0}</math>. It is also linear under multiplication by a positive vector. You can ====Linear independence of orthogonal vectors==== ...14 KB (2,162 words) - 08:28, 8 April 2010
- The last thing we talked about was the idea of a linear operator. Recall that In this lecture we will learn about adjoint operators, Jacobi tridiagonalization, ...12 KB (1,891 words) - 19:12, 26 August 2020
- [[Category:Linear operators]] ...3 KB (473 words) - 07:53, 4 June 2008
- ==Green's functions for linear differential operators== <math>n</math>th order linear differential operator we would want the <math>n</math>th derivative of ...4 KB (778 words) - 07:54, 4 June 2008
- Then we can write any arbitrary test function <math>\phi(x)</math> as a linear [[Category:Linear operators]] ...4 KB (708 words) - 18:16, 1 February 2010
Page text matches
- ...action on the function <math>\lambda_1 \Psi_1 + \lambda_2 \Psi_2</math>, a linear combination with constant (complex) coefficients, of two functions of this Among the linear operators acting on the [[../CosmologicalConstant2/|wave]] functions ...5 KB (744 words) - 03:42, 13 September 2020
- ...rProduct/|Hilbert space]] <math>\mathcal{H}</math>. For a [[../Commutator/|linear operator]] {\mathbf O} on <math>\mathcal{H}</math>, we denote its [[../Bije ...math> (such as the [[../Position/|position]] and [[../Momentum/|momentum]] operators, for example) is called a ''representation of the canonical commutation rel ...5 KB (694 words) - 04:54, 12 September 2020
- ==Green's functions for linear differential operators== <math>n</math>th order linear differential operator we would want the <math>n</math>th derivative of ...4 KB (778 words) - 07:54, 4 June 2008
- ...</math> is the <math>C^*</math>-algebra of bounded [[../Commutator/|linear operators]] on the Hilbert space <math>\mathbb{H}</math>; of course, one considers th ...1 KB (154 words) - 16:01, 12 September 2020
- ...when different than zero, it indicates the order of application of the two operators is important. The commutator of the operators <math>\hat{p}_x</math> and <math>\hat{p}_x^2</math> is zero (see Exercise) ...11 KB (1,849 words) - 01:17, 12 June 2020
- === The Linear Space and Wave Functions === ...ms which are listed below. Vector spaces are the basic objects of study in linear algebra, and are used throughout mathematics, science, and engineering. ...12 KB (1,859 words) - 18:01, 6 September 2015
- == Weak form of non-linear axial bar== Having discussed the equations of the non-linear axial bar, we proceed to construct a finite element approximation. ...4 KB (608 words) - 04:30, 1 January 2019
- ...nate and conjugate [[../Momentum/|momentum]] [[../QuantumOperatorAlgebra4/|operators]]. <math>X</math> and <math>P</math> satisfy the Heisenberg commutation/'un With these new dimensionless operators, <math>\mathbf{x}</math> and ...8 KB (1,066 words) - 08:36, 11 March 2023
- ...ath>\delta</math> symbol can be interpreted as a linear functional, i.e. a linear mapping from a [[../Bijective/|function]] space, consisting e.g. of certain ...ath>\delta</math>, can be correctly defined as a linear functional, i.e. a linear mapping from a function space, consisting e.g. of certain real functions, t ...3 KB (517 words) - 07:03, 23 October 2023
- ...h>, can be, however, correctly defined as a ''linear functional'' , i.e. a linear mapping from a function space, consisting e.g. of certain real functions, t L. H\"ormander, {\em The Analysis of Linear Partial Differential Operators I, ...3 KB (435 words) - 12:53, 11 October 2023
- ...h>\mathcal L(\bF (\mathcal{H}))</math> the bounded [[../Commutator/|linear operators]] on the Fock space <math>\bF (\mathcal{H})</math> of <math>\mathcal{H}</ma If <math>W</math> is an algebra and <math>c : V \lra W</math> is a linear map satisfying ...2 KB (399 words) - 09:49, 13 September 2020
- ...<math>|f\rangle</math> in <math>\mathfrak{H} </math> can be written as a linear combination of elements of <math>\{|k\rangle\}</math>. ...ngle f|</math> in <math>\mathfrak{H}^\dagger </math> can be written as a linear combination of elements of <math>\{\langle b|\}</math>. ...17 KB (2,660 words) - 19:03, 13 June 2018
- * how to build the operators corresponding to '''any''' observable; == How to build all operators == ...8 KB (1,424 words) - 01:18, 12 June 2020
- ...lence between the two statements that define the linearity of differential operators.<br> The definition of a linear operator, <math>\mathcal{D}</math>, is<br> ...9 KB (1,549 words) - 09:51, 27 August 2020
- which is linear in each factor and for which <math>\{STW\} = \{WTS\}</math>~. Certain examp An ''involution'' on a complex algebra <math>\mathfrak A</math> is a real--linear map <math>T \mapsto T^*,</math> such that for all <math>S, T \in \mathfrak ...10 KB (1,513 words) - 15:39, 12 September 2020
- if <math>\mathbf{x} = \mathbf{0}</math>. It is also linear under multiplication by a positive vector. You can ====Linear independence of orthogonal vectors==== ...14 KB (2,162 words) - 08:28, 8 April 2010
- Linear operators can be thought of as infinite dimensional matrices. Hence we can use well known results from matrix theory when dealing with linear operators. ...10 KB (1,661 words) - 19:04, 24 February 2025
- ...symbol{\nabla}_0 \bullet \boldsymbol{P}^T & = 0& & \qquad \text{Balance of Linear Momentum} \\ The gradient and divergence operators are defined such that ...6 KB (834 words) - 22:26, 25 July 2017
- [[Category:Linear operators]] ...3 KB (439 words) - 07:52, 4 June 2008
- ...um field theory]], and also in the theory of [[../QuantumOperatorAlgebra4/|operators]] on a [[../NormInducedByInnerProduct/|Hilbert space]]. An ''involution'' on a complex algebra <math>\mathfrak A</math> is a ''real--linear map'' <math>T \mapsto T^*</math> ...11 KB (1,607 words) - 05:03, 12 September 2020