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In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. For a vector , v → {\displaystyle {\vec {v}}\!} , adding two matrices would have the geometric effect of applying each matrix transformation separately onto v → {\displaystyle {\vec {v}}\!} , then adding the transformed vectors.
For example, the set of integers modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musical set theory. The set of integers modulo 2 has just two elements; the addition operation it inherits is known in Boolean logic as the "exclusive or" function.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
The characteristic function + = ((+)) of the sum of two independent random variables X and Y is just the product of the two separate characteristic functions: = (), = ()
The discovery of this pattern led Dalton to develop the modern theory of atoms, as it suggested that the elements combine with each other in multiples of a basic quantity. Along with the law of definite proportions , the law of multiple proportions forms the basis of stoichiometry .
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This makes it more difficult to combine the elements together. Compounds may be produced in a solid state reaction, by heating solids together, either in a vacuum or a gas. Common gases used include, oxygen, hydrogen, ammonia, chlorine, fluorine, hydrogen sulfide , or carbon disulfide.
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