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where is a nonsingular matrix with real entries and.
Let be an invertible Hermite matrix with real eigenvalues.
Assume that there exists a real diagonalization matrix with real eigenvalues satisfying (2.14) and commuting with.
Assume that there exists a real diagonalization matrix with real eigenvalues satisfying (2.13) and Denote (3.15).
Let A = ( a i j ) ∈ R n × n be an n × n matrix with real entries.
if there is a nonsingular matrix with real entries such that (1.6).
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The elimination/Chebyshev matrix (ECM) algorithm yields a companion matrix with real-valued elements, albeit at the price of usefulness only for real roots.
where P = Q ⊗ I3 is a sparse matrix with real-valued conversion[14], and matrix Q can be chosen for arrays with an even and odd number of sensors respectively by (16) and (17).
Using the QR decomposition, the channel matrix H can be transformed into the product of two matrices Q and R (H =QR), where Q is a N×M unitary matrix (Q H Q=I M ), and R is a M×M upper triangular matrix with real-positive entries on its diagonal.
Let us denote by Mn × nthe class of all n × n matrices with real elements.
A ( r ( t ) ) and B ( r ( t ) ) ∈ R n × n are matrices with real values in mode r ( t ).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
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CEO of Professional Science Editing for Scientists @ prosciediting.com