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A Frobenius matrix is a special kind of square matrix from numerical analysis. A matrix is a Frobenius matrix if it has the following three properties: all entries on the main diagonal are ones; the entries below the main diagonal of at most one column are arbitrary; every other entry is zero; The following matrix is an example.
The Frobenius norm is an extension of the Euclidean norm to and comes from the Frobenius inner product on the space of all matrices. The Frobenius norm is sub-multiplicative and is very useful for numerical linear algebra. The sub-multiplicativity of Frobenius norm can be proved using Cauchy–Schwarz inequality.
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.
Geometric interpretation of the angle between two ... The inner product for complex square matrices of the same size is the Frobenius ... Minkowski distance ...
The angle between two complex vectors is then given by ... Squared Euclidean distance). ... A double-dot product for matrices is the Frobenius inner product, ...
where ‖ ‖ denotes the Frobenius norm. This is a special case of Wahba's problem (with identical weights; instead of considering two matrices, in Wahba's problem the columns of the matrices are considered as individual vectors). Another difference is that Wahba's problem tries to find a proper rotation matrix instead of just an orthogonal one.
According to the Frobenius ... This norm makes it possible to define the distance d(p, q) between p and q as the ... as block diagonal matrices with two 2 × 2 ...
A matrix of scores which express the similarity between two data points: Sequence alignment: Sylvester matrix: A square matrix whose entries come from the coefficients of two polynomials: The Sylvester matrix is nonsingular if and only if the two polynomials are coprime to each other Symplectic matrix: The real matrix of a symplectic transformation