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Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of ...
If is a multi-index, and a is a positive real number, then | | (). Any smooth function f with compact support is in 𝒮(R n).This is clear since any derivative of f is continuous and supported in the support of f, so has a maximum in R n by the extreme value theorem.
The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills. [2] [3] [4] The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.
For a (0,2) tensor, [1] twice contracting with the inverse metric tensor and contracting in different indices raises each index: =. Similarly, twice contracting with the metric tensor and contracting in different indices lowers each index:
Multilinear algebra is the study of functions with multiple vector-valued arguments, with the functions being linear maps with respect to each argument. It involves concepts such as matrices, tensors, multivectors, systems of linear equations, higher-dimensional spaces, determinants, inner and outer products, and dual spaces.
{{Math templates | state = collapsed}} will show the template collapsed, i.e. hidden apart from its title bar. {{Math templates | state = autocollapse}} will show the template autocollapsed, i.e. if there is another collapsible item on the page (a navbox, sidebar, or table with the collapsible attribute), it is hidden apart from its title bar ...