singlenorm

Singlenorm is not a standardized term in mathematics or computer science. In published material, the phrase may be used informally to refer to a single norm selected for a given context, or to emphasize that a problem uses one norm term rather than a combination of norms. Because there is no universal definition, the meaning of singlenorm depends on the author and the context.

In mathematics, a norm on a vector space V is a function ||·|| from V to the nonnegative real numbers that satisfies positivity, scalability (homogeneity), and the triangle inequality. Common examples include the Euclidean norm (l2), the Manhattan norm (l1), and the maximum norm (linf). Any of these could be the “single norm” referenced in a discussion, depending on the context.

In optimization and data processing, a single norm may be used as the objective function or as a regularization term, for example minimizing ||x||2 or ||x||1. Discussions may contrast single-norm formulations with composite norms that combine multiple norm terms (such as elastic net, which blends l1 and l2).

If you encounter the term singlenorm in a text, consult the surrounding definitions to determine which norm is being referred to and whether the author intends a generic single-norm concept or a specific named norm used in a single context. As a nonstandard or context-dependent term, precise meaning is determined by the source.

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