Examples of 'singular values' in a sentence

Meaning of "singular values"

In the context of linear algebra and matrix theory, singular values are the positive square roots of the eigenvalues of a non-square matrix or the singular values of a rectangular matrix. They provide valuable information about the properties and behavior of a matrix, such as its rank, conditioning, and potential application in various mathematical and engineering problems. Singular values are widely used in fields like signal processing, data compression, and image recognition

How to use "singular values" in a sentence

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singular values
Singular values of functions in various particular cases.
The diagonal elements of w are the singular values of m.
Singular values and structured singular values.
The number of nonzero singular values is the rank of.
The singular values can accumulate only at zero.
The six largest singular values are.
Decomposition of the matrix in accordance with singular values.
In decomposing it into singular values of given numerical rank.
The diagonal entries of are known as the singular values of.
The singular values of a matrix are invariant under orthogonal transformations.
It can provide for singular values.
The singular values are related to another norm on the space of operators.
Therefore for each frequency there are eight singular values.
The rank of the matrix of singular values is then numerically fixed.
The eigenvalues are the squares of the required singular values.

See also

The notion of singular values can be extended from matrices to compact operators.
Where and are orthogonal and is a diagonal matrix containing the singular values.
Singular values are similar in that they can be described algebraically or from variational principles.
Choosing a large value for eps allows large variations in the singular values.
The p biggest singular values are average quadratic values of supply signals from different sources.
A is symmetric "eigenvalues and singular values are real.
Singular values and Lyapunov exponents are defined and their properties described.
However, it is well suited to applications that us only the first singular values.
The bouncing of the singular values is linked to the value of the poles S i.
In this case, the inverses of the smallest singular values are set to zero.
The singular values in A iu may be ordered from largest to smallest along the diagonal.
As there are five emitters, there are five singular values for each frequency.
Singular values related to the indicator matrix ;.
The rank of the training matrix is simply the number of non-zero singular values.
The p singular values assigned to the single scattering are determined iteratively as follows,.
The noise subspace was formed using the 13 smaller singular values of the covariance matrix estimate.
Non-zero singular values are simply the lengths of the semi-axes of this ellipsoid.
The result is too large to display here, but I can report the singular values.
This signature, constituted by the singular values of the object matrix, defines the recognition model.
One can easily verify the relationship between the Ky Fan 1-norm and singular values.
The total number of non-zero singular values is the rank of A.
Second, QR factorization can improve the quality of the eigenvectors associated with smaller singular values.
Assume n ≥ m and that the matrix G has the following singular values from SVD calculations, EPMATHMARKEREP.
The singular values from the S vector will be used for the SINR and sum-rate computation.
The Diagonal matrix S contains the non-negative, sorted singular values in its diagonal.
Or, equivalently, the singular values are the square roots of the eigenvalues.
Min-max theorem for singular values.
FIG . 16 shows the singular values as a function of the temporal frequency.
The size of the noise subspace has been set to the 13 smallest singular values.
Sylvester called the singular values the " canonical multipliers " of the matrix " A.
The columns of and are, respectively, left - and right-singular vectors for the corresponding singular values.
An example of temporal tracking of the singular values is given in FIG . 3 c.
Consequently, the above theorem implies that, An m × n matrix M has at most p distinct singular values.
FIG . 4 shows the modules of the singular values as a function of the frequency ;.
The singular values of a 2 × 2 matrix can be found analytically.

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