Similarity

Specific definitions

Different fields provide differing definitions of similarity:

In mathematics

In computer science

In other fields

See also

Matrix similarity

In linear algebra, two n-by-n matrices A and B are called similar if

for some invertible n-by-n matrix P. Similar matrices represent the same linear operator under two different bases, with P being the change of basis matrix.

A transformation is called a similarity transformation or conjugation of the matrix A. In the general linear group, similarity is therefore the same as conjugacy, and similar matrices are also called conjugate; however in a given subgroup H of the general linear group, the notion of conjugacy may be more restrictive than similarity, since it requires that P can be chosen to lie in H.

Properties

Similarity is an equivalence relation on the space of square matrices.

Similar matrices share any properties that are really properties of the represented linear operator:

Abyss (wrestler)

Christopher Joseph "Chris" Parks (born October 4, 1973), better known by his ring name Abyss, is an American professional wrestler currently signed with TNA. Parks along with James Storm are the only wrestlers currently employed by TNA to have appeared on the first broadcast.

As Abyss in TNA, Parks became a one-time NWA World Heavyweight Champion, being the first of only two men to hold the title while competing under a mask (Blue Demon, Jr. is the other). Abyss is the heaviest wrestler to hold the X Division Championship. He also captured the Television Championship twice, the NWA World Tag Team Championship once with A.J. Styles, and the TNA World Tag Team Championship once with James Storm as The Revolution. Having won all the required championships, Abyss was the fourth man to complete the Triple Crown Championship and the second to complete the Grand Slam Championship. Parks also wrestled in TNA as Abyss' storyline brother/split personality Joseph Park.

Early life

Chris Parks was born in Washington, D.C. He attended high school in Cleveland, Ohio, where he played football. He attended Ohio University, where he earned a master's degree in sports administration.

ABISMO

ABISMO (Automatic Bottom Inspection and Sampling Mobile) is a remotely operated underwater vehicle (ROV) built by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) for exploration of the deep sea. It is the only remaining ROV rated to 11,000-meters (after Nereus, built and operated by the Woods Hole Oceanographic Institution was lost at sea in 2014), ABISMO is intended to be the permanent replacement for Kaikō, a ROV that was lost at sea in 2003.

Kaikō

Between 1995 and 2003, Kaikō conducted more than 250 dives, collecting 350 biological species (including 180 different bacteria), some of which could prove to be useful in medical and industrial applications.Kaikō reached a maximum depth of 10,911.4 meters at the Challenger Deep on 24 March 1995, during its initial sea trials.Kaikō returned to Challenger Deep in February 1996, this time reaching a maximum depth of 10,898 meters.Kaikō made its last visit to Challenger Deep in May 1998. On 29 May 2003, Kaikō was lost at sea off the coast of Shikoku Island during Typhoon Chan-Hom, when a steel secondary cable connecting it to its launcher at the ocean surface broke. In May 2004, JAMSTEC resumed its research operations, using a converted ROV as its vehicle. This ROV, formerly known as UROV 7K, was rechristened Kaikō7000II. The 7000 designation indicates that this vessel is rated for diving to a maximum depth of 7,000 meters.