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  2. Vector-valued function - Wikipedia

    en.wikipedia.org/wiki/Vector-valued_function

    A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or greater than 1); the ...

  3. 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.

  4. Momentum - Wikipedia

    en.wikipedia.org/wiki/Momentum

    The kinetic energy equations are exceptions to the above replacement rule. The equations are still one-dimensional, but each scalar represents the magnitude of the vector, for example, = + +. Each vector equation represents three scalar equations.

  5. Jacobian matrix and determinant - Wikipedia

    en.wikipedia.org/wiki/Jacobian_matrix_and...

    In vector calculus, the Jacobian matrix (/ dʒ ə ˈ k oʊ b i ə n /, [1] [2] [3] / dʒ ɪ-, j ɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.

  6. Curl (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Curl_(mathematics)

    so the curl of a 1-vector field (fiberwise 4-dimensional) is a 2-vector field, which at each point belongs to 6-dimensional vector space, and so one has = < =,,,,, which yields a sum of six independent terms, and cannot be identified with a 1-vector field. Nor can one meaningfully go from a 1-vector field to a 2-vector field to a 3-vector field ...

  7. Equations of motion - Wikipedia

    en.wikipedia.org/wiki/Equations_of_motion

    There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.

  8. Eigenvalues and eigenvectors - Wikipedia

    en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

    which can be found by stacking into matrix form a set of equations consisting of the above difference equation and the k – 1 equations =, …, + = +, giving a k-dimensional system of the first order in the stacked variable vector [+] in terms of its once-lagged value, and taking the characteristic equation of this system's matrix.

  9. Singular value decomposition - Wikipedia

    en.wikipedia.org/wiki/Singular_value_decomposition

    The geometric content of the SVD theorem can thus be summarized as follows: for every linear map ⁠: ⁠ one can find orthonormal bases of ⁠ ⁠ and ⁠ ⁠ such that ⁠ ⁠ maps the ⁠ ⁠-th basis vector of ⁠ ⁠ to a non-negative multiple of the ⁠ ⁠-th basis vector of ⁠, ⁠ and sends the leftover basis vectors to zero.