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Q: How can you compute the inverse of a matrix by cayley hamilton theorem?

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Not really. There was no notable person with that name although it is possible that there are (were) people with that name. The Cayley–Hamilton theorem is named, not after a person called Cayley Hamilton, but after TWO mathematicians: Arthur Cayley and William Rowan Hamilton.

cayley did addition and divisen I know that because I'm cayley

George Cayley was born in Scarborough, Yorkshire in 1733.

he invented airfoil

a flying machine glider

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The Cayley-Hamilton (not Caley hamilton) theorem allows powers of the matrix to be calculated more simply by using the characteristic function of the matrix. It can also provide a simple way to calculate the inverse matrix.

Not really. There was no notable person with that name although it is possible that there are (were) people with that name. The Cayley–Hamilton theorem is named, not after a person called Cayley Hamilton, but after TWO mathematicians: Arthur Cayley and William Rowan Hamilton.

Cayley's Theorem states that every group G is isomorphic to a subgroup of the symmetric group on G.

cayley did addition and divisen I know that because I'm cayley

Richard Cayley was born in 1833.

Charles Cayley died in 1883.

Charles Cayley was born in 1823.

Cayley Baronets was created in 1661.

Michael Cayley died in 1878.

Michael Cayley was born in 1842.

Richard Cayley died in 1908.

Sir G. Cayley has written: 'Aeronautical and miscellaneous note-book (ca. 1799-1826) of Sir George Cayley, with...a list of the Cayley papers'