Similar Matrices

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similar matrices

[¦sim·i·lər ′mā·tri‚sēz]
(mathematics)
Two square matrices A and B related by the transformation B = SAT, where S and T are nonsingular matrices and T is the inverse matrix of S.

Similar Matrices

 

Two square matrices A and B of order n are said to be similar if there exists a nonsingular, or invertible, matrix P of order n such that B= P-1AP. Similar matrices are obtained when the matrix of a linear transformation is given in different coordinate systems. The role of the matrix P in this case is played by the matrix of the transformation of coordinates. For a given matrix A it is often important to select a second matrix B that is similar to A and has as simple a form as possible—for example, the Jordan matrix. Similar matrices are of identical rank. The characteristic polynomials ǀ λEAǀ and ǀλEBǀ and, consequently, the determinants ǀA and ǀBǀ and the eigenvalues of the similar matrices A and B coincide.

References in periodicals archive ?
A similar matrix is devised in order to match the user activity log and its pattern in a transformed space.
Usually, these allow the PCR reaction to diffuse across a paper or similar matrix test strip, which is spotted or coated with antibodies to the hapten at specific places.
Though their stories would unfold independent of one another," explains English, "all three men became enmeshed in a similar matrix of forces--political, social, and racial--that would alter the direction of the city.
Using a similar matrix concept, Decision Technology produces a Product Attribute Ratio (PAR), which can be plotted on a positioning graph.
In the 1960s Ansoff's notion of competence (which was later developed by Hamel and Prahalad) was not unique, and although Ansoff seems to have been the originator of his 2 x 2 growth vector component matrix, a similar matrix had been published earlier.
According to this report, resonant frequency or ultrasonic velocity measurements can be used to predict the effect of small changes in graphite form on the tensile strength, offset yield strength and other properties of ductile iron castings of known similar matrix structure containing up to 70% non-nodular graphite.
A similar matrix for purchasers of RTA furniture at discount stores shows that about one-third (31.
However, in a similar matrix crossing soft/hard states with (Ibn Khaldunian) strong/weak states, Jordan occupies the soft/weak box.
However, it is possible to develop a similar matrix just as relevant to CPA firms.
It may provoke your thinking as to how you should construct a similar matrix with specifics that fit your situation before you alter an existing nonwoven production line or before designing a new one.
patent 7,591,426 enables the reading and writing of data to take place on magnetic stripes using a similar matrix to the patent described above.