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In SGML, HTML and XML documents, the logical constructs known as character data and attribute values consist of sequences of characters, in which each character can manifest directly (representing itself), or can be represented by a series of characters called a character reference, of which there are two types: a numeric character reference and a character entity reference.
In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator acting on an inner product space is called positive-semidefinite (or non-negative) if, for every (), , and , , where is the domain of .
These special sequences are character references. Character references that are based on the referenced character's UCS or Unicode code point are called numeric character references. In HTML 4 and in all versions of XHTML and XML, the code point can be expressed either as a decimal (base 10) number or as a hexadecimal (base 16) number. The ...
In mathematics, positive semidefinite may refer to: Positive semidefinite function; Positive semidefinite matrix; Positive semidefinite quadratic form;
A numeric character reference in HTML refers to a character by its Universal Character Set/Unicode code point, and uses the format &#nnnn; or &#xhhhh; where nnnn is the code point in decimal form, and hhhh is the code point in hexadecimal form. The x must be lowercase in XML documents.
HTML and XML provide ways to reference Unicode characters when the characters themselves either cannot or should not be used. A numeric character reference refers to a character by its Universal Character Set/Unicode code point, and a character entity reference refers to a character by a predefined name. A numeric character reference uses the ...
This implies that at a local minimum the Hessian is positive-semidefinite, and at a local maximum the Hessian is negative-semidefinite. For positive-semidefinite and negative-semidefinite Hessians the test is inconclusive (a critical point where the Hessian is semidefinite but not definite may be a local extremum or a saddle point).
U and P commute, where we have the polar decomposition A = UP with a unitary matrix U and some positive semidefinite matrix P. A commutes with some normal matrix N with distinct [clarification needed] eigenvalues. σ i = | λ i | for all 1 ≤ i ≤ n where A has singular values σ 1 ≥ ⋯ ≥ σ n and has eigenvalues that are indexed with ...