The invertible matrix A ∈ H 0 + ( n ) implies A ∈ H + ( n ), thus the set of invertible matrices C H + ( n ) ⊂ H + ( n ).
Define the transformed HMM parameters (5) Then we can compute the transformed latent feature as (6) since the invertible matrix cancels with during matrix multiplication.
By using the above elementary invertible linear transformations, the augmented matrix [ A | T ] transforms into row-echelon form, which yields (2.3) from the last low.
Finding the optimal weights for, using standard least-squares fitting, requires a well-conditioned invertible matrix, which we ensure using a custom-designed regularization technique of adding a small fraction to the diagonal elements of the correlation matrix.
Interestingly, an iGEM team from Davidson University has already considered using the possible computational power of a single invertible system as a means of solving a combinatorial problem [25].
Finally, for an invertible matrix D we will use the norm begin{aligned} Vert D Vert =sup_{xinmathbb {R}^{n},xneq0}frac{ vert Dx vert }{ vert x vert }. end{aligned} (2.1) Then it is easy to see that begin{aligned} begin{aligned} Vert D Vert ^{-n}le biglvert detbigl(D^{-1}bigr) bigrvert le biglVert D^{-1} bigrVert ^{n}.
The system of equations obtained in Eq. (9) from Eq. (7) saves computation time by inverting a much smaller, directly invertible matrix and limits the source space domain by considering only the eigenvectors that contribute to the source distribution.
There are symmetric cryptosystems in which the encryption and decryption keys are not the same for example, matrix transforms of the text in which one key is a nonsingular (invertible) matrix and the other its inverse.
Using quadratic form theory, we can know that ((A_{2}+G^{-1})) is an invertible matrix, and problem (38) has a unique solution by the theory of differential equations.
Finally, recall that this invertible matrix in the most general form is given by a combination of steady-state assumptions and the sum containing the conserved moiety.
