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  2. Lists of vector identities - Wikipedia

    en.wikipedia.org/wiki/Lists_of_vector_identities

    There are two lists of mathematical identities related to vectors: Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc.

  3. Dot product - Wikipedia

    en.wikipedia.org/wiki/Dot_product

    The length of a vector is defined as the square root of the dot product of the vector by itself, and the cosine of the (non oriented) angle between two vectors of length one is defined as their dot product. So the equivalence of the two definitions of the dot product is a part of the equivalence of the classical and the modern formulations of ...

  4. Hadamard product (matrices) - Wikipedia

    en.wikipedia.org/wiki/Hadamard_product_(matrices)

    The NumPy numerical library interprets a*b or a.multiply(b) as the Hadamard product, and uses a@b or a.matmul(b) for the matrix product. With the SymPy symbolic library, multiplication of array objects as either a*b or a@b will produce the matrix product. The Hadamard product can be obtained with the method call a.multiply_elementwise(b). [22]

  5. Basic Linear Algebra Subprograms - Wikipedia

    en.wikipedia.org/wiki/Basic_Linear_Algebra...

    Initially, these subroutines used hard-coded loops for their low-level operations. For example, if a subroutine needed to perform a matrix multiplication, then the subroutine would have three nested loops. Linear algebra programs have many common low-level operations (the so-called "kernel" operations, not related to operating systems). [14]

  6. Vector multiplication - Wikipedia

    en.wikipedia.org/wiki/Vector_multiplication

    The dot product of two vectors can be defined as the product of the magnitudes of the two vectors and the cosine of the angle between the two vectors. Alternatively, it is defined as the product of the projection of the first vector onto the second vector and the magnitude of the second vector.

  7. Outer product - Wikipedia

    en.wikipedia.org/wiki/Outer_product

    The outer product contrasts with: The dot product (a special case of "inner product"), which takes a pair of coordinate vectors as input and produces a scalar; The Kronecker product, which takes a pair of matrices as input and produces a block matrix; Standard matrix multiplication

  8. Inner product space - Wikipedia

    en.wikipedia.org/wiki/Inner_product_space

    Product of vectors in Minkowski space is an example of indefinite inner product, although, technically speaking, it is not an inner product according to the standard definition above. Minkowski space has four dimensions and indices 3 and 1 (assignment of "+" and "−" to them differs depending on conventions ).

  9. Array programming - Wikipedia

    en.wikipedia.org/wiki/Array_programming

    The cross product operation is an example of a vector rank function because it operates on vectors, not scalars. Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing ...