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Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication.
The cross product with respect to a right-handed coordinate system. In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol .
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.
Cross product – also known as the "vector product", a binary operation on two vectors that results in another vector. The cross product of two vectors in 3-space is defined as the vector perpendicular to the plane determined by the two vectors whose magnitude is the product of the magnitudes of the two vectors and the sine of the angle ...
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.
Matrix multiplication completed in 2n-1 steps for two n×n matrices on a cross-wired mesh. There are a variety of algorithms for multiplication on meshes . For multiplication of two n × n on a standard two-dimensional mesh using the 2D Cannon's algorithm , one can complete the multiplication in 3 n -2 steps although this is reduced to half ...
A coordinate vector is commonly organized as a column matrix (also called a column vector), which is a matrix with only one column. So, a column vector represents both a coordinate vector, and a vector of the original vector space. A linear map A from a vector space of dimension n into a vector space of dimension m maps a column vector
The logical operation and takes the place of multiplication. The outer product of two logical vectors (u i) and (v j) is given by the logical matrix () = (). This type of matrix is used in the study of binary relations, and is called a rectangular relation or a cross-vector. [12]