English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This form is very convenient since the multiplication of matrices is performed by an electronic computer in almost no time. The unitary matrices U and T are known to exist (for example modal matrices of G*G' and *G'G), but the question how to form them for a given complex matrix G of large order is a difficult one. In what follows they are formed as infinite convergent products of simple unitary matrices un{zn) which represent plane rotations through complex angles z„ = 9n + in . Therefore, their practical computation is easy for electronic equipment and it yields a new method of solution of linear systems. When this method is applied to a Hermitian system Hx = h or to a symmetric system of real equation (particular case of Hx = h) the diagonal matrix K into which H is transformed has as its elements the characteristic roots (Eigenvalues) of H, while U = T yields the characteristic vectors, because K = *U'HU. The same holds for skew symmetric Hermitian matrices [(ar, + t'6r,)] with br, = b,r , aT, + a,r = 0. To achieve the diagonalization of a given complex matrix A = A0 a sequence [A„] of its transforms is constructed, the transform A,being formed from A,--! by right and left multiplications:

Solution of linear equations by diagonalization of coefficients matrix