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Sturm–Liouville form or self-adjoint form. All second-order linear homogenous ordinary differential equations can be recast in the form on the left-hand...

In mathematics, a self-adjoint operator on a complex vector space V with inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is a linear...

perspective. Examples of operators to which the spectral theorem applies are self-adjoint operators or more generally normal operators on Hilbert spaces. The spectral...

{\displaystyle A} on an inner product space defines a Hermitian adjoint (or adjoint) operator A ∗ {\displaystyle A^{*}} on that space according to the...

variable. The adjoint method formulates the gradient of a function towards its parameters in a constraint optimization form. By using the dual form of this...

Every self-adjoint operator is maximal symmetric. The converse is wrong. An operator is called essentially self-adjoint if its closure is self-adjoint. An...

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element...

transpose may be seen to be independent of any bilinear form on the modules, unlike the adjoint (below). The continuous dual space of a topological vector...

Martians (scientists) Lanczos, Cornelius (1958). "Linear Systems in Self-Adjoint Form". Amer. Math. Monthly. 65 (9): 665–679. doi:10.2307/2308707. JSTOR 2308707...

An adjoint equation is a linear differential equation, usually derived from its primal equation using integration by parts. Gradient values with respect...

be two homogeneous linear second order differential equations in self-adjoint form with 0 < p 2 ( x ) ≤ p 1 ( x ) {\displaystyle 0<p_{2}(x)\leq p_{1}(x)}...

f(x)\cdot x=0} for every x ∈ R 2 {\displaystyle x\in \mathbb {R} ^{2}} . A self-adjoint operator A : H → H , {\displaystyle A:H\to H,} where H {\displaystyle...

the adjoint operator. When T ∗ {\displaystyle T^{*}} is defined according to this formula, it is called the formal adjoint of T. A (formally) self-adjoint...

form F A {\displaystyle F_{A}} , which is a two-form on X {\displaystyle X} with values in the adjoint bundle ad ⁡ ( P ) {\displaystyle \operatorname {ad}...

thought of as skew-adjoint (since they are like 1 × 1 {\displaystyle 1\times 1} matrices), whereas real numbers correspond to self-adjoint operators. For...

In functional analysis, the Friedrichs extension is a canonical self-adjoint extension of a non-negative densely defined symmetric operator. It is named...

isomorphism. Self-adjoint elements are those of the form x = x ∗ {\displaystyle x=x^{*}} . The set of elements of a C*-algebra A of the form x ∗ x {\displaystyle...

constructions, of self-adjoint extensions. This problem arises, for example, when one needs to specify domains of self-adjointness for formal expressions...

presented under the self-adjoint form, a more tractable equation for the ray head position vector r is given in generic parametric form: r ¨ = n grad ⁡ n...

operators (i.e., self-adjoint operators): N* = N skew-Hermitian operators: N* = −N positive operators: N = MM* for some M (so N is self-adjoint). A normal matrix...