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Note that all the elements of this matrix are positive.
Notice that the elements of the leading diagonal of the consistent mass matrix are positive.
The principal eigenvector is the eigenvector corresponding to the largest eigenvalue (principal eigenvalue) of the adjacency matrix, A. Moreover, if all the entries in a square matrix are positive (i.e., greater than or equal to zero), the principal eigenvalue as well as the entries in the principal eigenvector are also positive [6].
Constraints that relate data points, i and j, in two different datasets are represented via two constraint matrices, Θ 1 ∈ R n 1 × n 1 and Θ 2 ∈ R n 2 × n 2. Entries of the constraint matrix are positive for dissimilar data objects because they impose penalties on the current approximation given in the Equation (1).
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Furthermore, a matrix is positive is all its entries are positive (greater than zero) real numbers.
We focus in this paper on the special case where the system matrix is positive definite (and hence the system is completely unstable).
For meshes of polyhedra whose faces have not more than four edges, the associated matrix is positive definite (and symmetric if the diffusion tensor is symmetric).
Hence, the given matrix is positive semidefinite.
so the matrix is positive semi-definite.
Assume that matrix is positive definite.
Because all eigenvalues are positive, matrix is positive definite.
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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.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com