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In general, the value of the norm is dependent on the spectrum of : For a vector with a Euclidean norm of one, the value of ‖ ‖ is bounded from below and above by the smallest and largest absolute eigenvalues of respectively, where the bounds are achieved if coincides with the corresponding (normalized) eigenvectors.
Norms provide rules for behavior in specific situations, while values identify what should be judged as good or evil. While norms are standards, patterns, rules and guides of expected behavior, values are abstract concepts of what is important and worthwhile. Flying the national flag on a holiday is a norm, but it reflects the value of patriotism.
The standard absolute value on the integers. The standard absolute value on the complex numbers.; The p-adic absolute value on the rational numbers.; If R is the field of rational functions over a field F and () is a fixed irreducible polynomial over F, then the following defines an absolute value on R: for () in R define | | to be , where () = () and ((), ()) = = ((), ()).
These values and units of socialization thus act to encourage or enforce social activity and outcomes that ought to (with respect to the norms implicit in those structures) occur, while discouraging or preventing social activity that ought not occur. That is, they promote social activity that is socially valued (see philosophy above).
Suppose a vector norm ‖ ‖ on and a vector norm ‖ ‖ on are given. Any matrix A induces a linear operator from to with respect to the standard basis, and one defines the corresponding induced norm or operator norm or subordinate norm on the space of all matrices as follows: ‖ ‖, = {‖ ‖: ‖ ‖ =} = {‖ ‖ ‖ ‖:} . where denotes the supremum.
The methodological basis for positive/normative distinction is rooted in the fact-value distinction in philosophy. A positive statement is an assertion about facts of the world, while normative statements express value judgments. The former describe the world as it is, while the latter talk about the world as it should be. [3]
A convention influences a set of agreed, stipulated, or generally accepted standards, social norms, or other criteria, often taking the form of a custom.. In physical sciences, numerical values (such as constants, quantities, or scales of measurement) are called conventional if they do not represent a measured property of nature, but originate in a convention, for example an average of many ...
Norms differ for each class because the members of each class were raised differently and hold different sets of values. Tension can form, therefore, between the upper class and lower class when laws and rules are put in place that do not conform to the values of both classes.