logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm....

{1}{\sqrt {m}}}\|A\|_{1}\leq \|A\|_{2}\leq {\sqrt {n}}\|A\|_{1}.} Dual norm Logarithmic norm The condition only applies when the product is defined, such as...

Richter scale of earthquake intensity. Logarithmic magnitudes can be negative. In the natural sciences, a logarithmic magnitude is typically referred to as...

P(\rho )} is an arbitrary LOCC operation over ρ {\displaystyle \rho } The logarithmic negativity is an entanglement measure which is easily computable and...

Stochastic Gronwall inequality Logarithmic norm, for a version of Gronwall's lemma that gives upper and lower bounds to the norm of the state transition matrix...

usually marked with an "A" for logarithmic taper or a "B" for linear taper; "C" for the rarely seen reverse logarithmic taper. Others, particularly those...

Hörmander as his advisors. As part of this work he introduced the logarithmic norm (also introduced by Russian mathematician Sergei Lozinskii the same...

In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient ∇ f {\displaystyle...

f ( x ^ ) = 0 {\displaystyle f({\hat {x}})=0} . If there exists a logarithmic norm μ {\displaystyle \mu } such that the Jacobian J ( x ) = D x f {\displaystyle...

It represents a logarithmic plot where the norm of a regularized solution is plotted against the norm of the corresponding residual norm. It is useful for...

measure on the real numbers under the logarithm: it is the length on the logarithmic scale. In fact, it is an invariant measure with respect to multiplication...

other more complex definitions of strain are required, such as stretch, logarithmic strain, Green strain, and Almansi strain. Engineering strain, also known...

arithmetic to the geometric composition of angles. Marking the line with logarithmically spaced graduations associates multiplication and division with geometric...

of the logarithmic derivative of f {\displaystyle f} , which is ( log ⁡ f ) ′ = f ′ / f {\displaystyle (\log f)'=f'/f} , and the logarithmic derivative...

of norms in finite dimensions, a topologically equivalent metric is obtained if N is the taxicab norm, a p-norm, the maximum norm, or any other norm which...

Logarithmic chart of the hearing ranges of some animals...

form of a logarithmic spiral) using quarter-circles with radii from these sequences, differing only slightly from the true golden logarithmic spiral. Fibonacci...

precise estimate may be given in terms of the logarithmic integral function. The number of prime ideals of norm ≤ X is L i ( X ) + O K ( X exp ⁡ ( − c K log...

associated with a norm called the Euclidean norm, defined as the distance of each vector from the origin. One of the important properties of this norm, relative...

there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding...

property above, x = ƒ(t). The order of growth of Dirichlet's kernel is logarithmic, i.e. ∫ | D N ( t ) | d t = 4 π 2 log ⁡ N + O ( 1 ) . {\displaystyle...

comparison to the reference level of 1 pPa (= 10−12 pascals). It is a logarithmic measure of the ratio of two sound energy densities. The unit of the sound...

removed. This 2-norm in logarithmic space can be generalized to p-norm in logarithmic space. The drawback of this 2-norm in logarithmic space is that it...

When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so...

closed-form solutions for arc length include the catenary, circle, cycloid, logarithmic spiral, parabola, semicubical parabola and straight line. The lack of...

n=2} the term bidisc is sometimes used. A polydisc is an example of logarithmically convex Reinhardt domain. Poincare, H, Les fonctions analytiques de...

expected frequency: points that fall more than 3 standard deviations from the norm are likely outliers (unless the sample size is significantly large, by which...

the logarithmic characteristics of the power spectra, and it becomes effective when the processing task of the power spectrum also has logarithmic characteristics...

of oil, water and gas within porous rock at very high pressure. pH A logarithmic measure of the concentration of hydrogen ions in an acid or base solution...

of the coordinates (e.g. 7 for the coordinates (3/7, 1/2)), but in a logarithmic scale. Height functions allow mathematicians to count objects, such as...