Sentence examples for matrices we deduce from inspiring English sources

For an AB-multiresolution analysis associated with any expanding matrices, we deduce that there exists a singe scaling function in its reducing subspace.

In this section we obtain some estimates or identities for the operator norms of certain matrix operators and we deduce the necessary and sufficient conditions for such operators to be compact.

Initiated by the analysis of phase relationship and by use of the films' characteristic matrix expression, we deduced two implicit function expressions of the spacer' moderate refractive index as well as P-polarization and S-polarization' central wavelengths.

Using the above-mentioned results, we deduce the matrix analogue of the trace formula for finite-zone matrix potentials.

Then from the theory of linear algebra we deduce that the matrix (1) is a diagonalizable.

In Sect. 3 we deduce a new matrix interpretation of the recurrence relation satisfied by the polynomial sequence ((hat{B}_{n})_ {n=0}^{infty }) in terms of a matrix polynomial of the Jacobi matrix associated with the sequence of orthonormal polynomials ((p_n)_{n=0}^{infty }).

We deduce that the correlation matrix of z is: Φ z = Φ x fd + Φ v rn, (6).

we deduce.

What more can we deduce?

So what can we deduce?

Finally, we deduce (3.8).