- List of zero terms
The number 0 is an important concept in
mathematics, the zero module is the module consisting of only the additive identity for the module's additionfunction. In the integers, this identity is zero, which gives the name "zero module". That the zero module is in fact a module is simple to show; it is closed under addition and multiplicationtrivially.
The set of "m"×"n" matrices with entries in a ring K forms a ring . The zero matrix in is the matrix with all entries equal to , where is the additive identity in K.
The zero matrix is the additive identity in . That is, for all it satisfies
There is exactly one zero matrix of any given size "m"×"n" having entries in a given ring, so when the context is clear one often refers to "the" zero matrix. In general the zero element of a ring is unique and typically denoted as 0 without any subscript indicating the parent ring. Hence the examples above represent zero matrices over any ring.
The zero matrix represents the
linear transformationsending all vectors to the zero vector.
mathematics, the zero tensor is any tensor, of any rank, all of whose entries are zero. The zero tensor of rank 1 is sometimes known as the null vector.
tensor productof any tensor with any zero tensor results in another zero tensor. Adding the zero tensor is equivalent to the identity operation.
zero divisorin a ring "R" is an element "a" ∈ "R" such that "ab" = 0 for some non-zero "b" ∈ "R".
abstract algebra, an additive monoidis said to be zerosumfree if nonzero elements do not sum to zero. Formally:
This means that the only way zero can be expressed as a sum is as .
mathematics, the zero setof a real-valued function "f" is the inverse image .
A zero order process is one in which past behavior does not affect the future outcome. For example, in
marketing, the zero order hypothesisholds that the brands you will purchase next will not depend on the brands you have purchased before. That means you have a fixed probabilityof purchase. Contrast it to the first orderprocess when the outcome at time "t"-1 changes the outcome at time "t".
Zero of a function
*Zero non mathematical uses.
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