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  2. Minkowski addition - Wikipedia

    en.wikipedia.org/wiki/Minkowski_addition

    For Minkowski addition, the zero set, {}, containing only the zero vector, 0, is an identity element: for every subset S of a vector space, S + { 0 } = S . {\displaystyle S+\{0\}=S.} The empty set is important in Minkowski addition, because the empty set annihilates every other subset: for every subset S of a vector space, its sum with the ...

  3. Euclidean vector - Wikipedia

    en.wikipedia.org/wiki/Euclidean_vector

    In such a case it is necessary to develop a method to convert between bases so the basic vector operations such as addition and subtraction can be performed. One way to express u , v , w in terms of p , q , r is to use column matrices along with a direction cosine matrix containing the information that relates the two bases.

  4. Matrix addition - Wikipedia

    en.wikipedia.org/wiki/Matrix_addition

    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.

  5. Vector (mathematics and physics) - Wikipedia

    en.wikipedia.org/wiki/Vector_(mathematics_and...

    Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2w . In mathematics and physics , a vector space (also called a linear space) is a set whose elements, often called vectors , can be added together and multiplied ...

  6. Vector space - Wikipedia

    en.wikipedia.org/wiki/Vector_space

    Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2 w . In mathematics and physics , a vector space (also called a linear space ) is a set whose elements, often called vectors , can be added together and multiplied ...

  7. Computational complexity of mathematical operations - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.

  8. Vector algebra relations - Wikipedia

    en.wikipedia.org/wiki/Vector_algebra_relations

    The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.

  9. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    Addition, subtraction and multiplication of complex numbers can be naturally defined by using the rule = along with the associative, commutative, and distributive laws. Every nonzero complex number has a multiplicative inverse. This makes the complex numbers a field with the real numbers as a subfield.

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