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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 distributions, by generalising the concept of an integer index to an ordered tuple of indices.
The entry of a matrix A is written using two indices, say i and j, with or without commas to separate the indices: a ij or a i,j, where the first subscript is the row number and the second is the column number. Juxtaposition is also used as notation for multiplication; this may be a source of confusion. For example, if
Terms inside the bracket are evaluated first; hence 2×(3 + 4) is 14, 20 ÷ (5(1 + 1)) is 2 and (2×3) + 4 is 10. This notation is extended to cover more general algebra involving variables: for example (x + y) × (x − y). Square brackets are also often used in place of a second set of parentheses when they are nested—so as to provide a ...
the digit "ten" in hexadecimal [2] and other positional numeral systems with a radix of 11 or greater [3] the unit ampere for electric current in physics [4] the area of a figure [5] the mass number or nucleon number of an element in chemistry [6] the Helmholtz free energy of a closed thermodynamic system of constant pressure and temperature [7]
Also supports Microsoft Word equations, Wolfram Alpha to see the computation results and answers, MathJax, Google Docs equations, MathType equations, Wiki equations, AsciiMathML, and Text-To-Speech to read out math expressions. Personal Edition is for general purpose use.
Convolution is used to add two independent random variables defined by distribution functions. Its usual definition combines integration, subtraction, and multiplication. [96] In general, convolution is useful as a kind of domain-side addition; by contrast, vector addition is a kind of range-side addition.
It is common convention to use greek indices when writing expressions involving tensors in Minkowski space, while Latin indices are reserved for Euclidean space. Well-formulated expressions are constrained by the rules of Einstein summation : any index may appear at most twice and furthermore a raised index must contract with a lowered index.
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures