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  2. Row and column vectors - Wikipedia

    en.wikipedia.org/wiki/Row_and_column_vectors

    In linear algebra, a column vector with ⁠ ⁠ elements is an matrix [1] consisting of a single column of ⁠ ⁠ entries, for example, = [].. Similarly, a row vector is a matrix for some ⁠ ⁠, consisting of a single row of ⁠ ⁠ entries, = […]. (Throughout this article, boldface is used for both row and column vectors.)

  3. Tensor derivative (continuum mechanics) - Wikipedia

    en.wikipedia.org/wiki/Tensor_derivative...

    The derivatives of scalars, vectors, and second-order tensors with respect to second-order tensors are of considerable use in continuum mechanics.These derivatives are used in the theories of nonlinear elasticity and plasticity, particularly in the design of algorithms for numerical simulations.

  4. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    In Cartesian coordinates, the divergence of a continuously differentiable vector field = + + is the scalar-valued function: ⁡ = = (, , ) (, , ) = + +.. As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge.

  5. Frobenius inner product - Wikipedia

    en.wikipedia.org/wiki/Frobenius_inner_product

    In mathematics, the Frobenius inner product is a binary operation that takes two matrices and returns a scalar.It is often denoted , .The operation is a component-wise inner product of two matrices as though they are vectors, and satisfies the axioms for an inner product.

  6. Linear form - Wikipedia

    en.wikipedia.org/wiki/Linear_form

    If V is a vector space over a field k, the set of all linear functionals from V to k is itself a vector space over k with addition and scalar multiplication defined pointwise. This space is called the dual space of V, or sometimes the algebraic dual space, when a topological dual space is also considered.

  7. Matrix calculus - Wikipedia

    en.wikipedia.org/wiki/Matrix_calculus

    In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.

  8. Covariance and contravariance of vectors - Wikipedia

    en.wikipedia.org/wiki/Covariance_and_contra...

    A scalar (also called type-0 or rank-0 tensor) is an object that does not vary with the change in basis. An example of a physical observable that is a scalar is the mass of a particle. The single, scalar value of mass is independent to changes in basis vectors and consequently is called invariant.

  9. Linear span - Wikipedia

    en.wikipedia.org/wiki/Linear_span

    The cross-hatched plane is the linear span of u and v in both R 2 and R 3, here shown in perspective.. In mathematics, the linear span (also called the linear hull [1] or just span) of a set of elements of a vector space is the smallest linear subspace of that contains .