Synonyms for scalar_valued or Related words with scalar_valued

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Examples of "scalar_valued"
This form can be seen as a generalization of the scalar-valued variance to higher dimensions. Recall that for a scalar-valued random variable "X"
The scalar-valued variance is defined correspondingly:
A matrix polynomial is a polynomial with matrices as variables. Given an ordinary, scalar-valued polynomial
then the scalar-valued covariance (denoted by COVV) is defined by
The general expressions for a scalar-valued function, "f", are a little simpler.
A scalar-valued function on a Cartesian product (or direct sum) of vector spaces
If is a scalar valued function and is a vector field, then
A basic example of maps between manifolds are scalar-valued functions on a manifold,
The Jacobian generalizes the gradient of a scalar-valued function of multiple variables, which itself generalizes the derivative of a scalar-valued function of a single variable. In other words, the Jacobian for a scalar-valued multivariate function is the gradient and that of a scalar-valued function of single variable is simply its derivative. The Jacobian can also be thought of as describing the amount of "stretching", "rotating" or "transforming" that a transformation imposes locally. For example, if is used to transform an image, the Jacobian , describes how the image in the neighborhood of is transformed.
A function is Pettis integrable (over formula_25) if the scalar-valued function formula_26 is integrable for every functional formula_27.
The variance of a complex scalar-valued random variable with expected value μ is conventionally defined using complex conjugation:
This can be split into the symmetric, scalar valued, interior product and the antisymmetric, bivector valued, exterior product:
This is analogous to the notion of strictly increasing for scalar-valued functions of one scalar argument.
As in the scalar valued case, the exponential family is said to be in canonical form if
Examples of decomposable operators are those defined by scalar-valued (i.e. C-valued) measurable functions λ on "X". In fact,
where formula_44 is the Euclidean norm. For the case when switching function formula_52 is scalar valued, the sufficient condition becomes
In mathematics, a relative scalar (of weight "w") is a scalar-valued function whose transform under a coordinate transform,
This can be split into the symmetric, scalar valued, interior product and an antisymmetric, bivector valued exterior product:
In mathematics, a matrix polynomial is a polynomial with matrices as variables. Given an ordinary, scalar-valued polynomial
The vector-parameter form over a single scalar-valued random variable can be trivially expanded to cover a joint distribution over a vector of random variables. The resulting distribution is simply the same as the above distribution for a scalar-valued random variable with each occurrence of the scalar "x" replaced by the vector