Directly across from the Gardens I found a bus stop sign for T 4 and rode it down to the Bosphorus, with the sports center on my left just before I reached the water and the entrance to Dolmabahce Palace immediately after that.

He also bought a huge square of pegboard for hanging up his tools, and lumber for his workbench, sandpaper and glue and assorted nails, levels and T squares and plumb lines and several gadgets that he had no idea how to use or what they were for.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

The lines are asymmetric and over the range of field Af gauss and temperature Af the asymmetry increases with increasing Af and decreasing T.

We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.

We can do this through the characteristic values and vectors of T in certain special cases, i.e., when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1.

If we try to study T using characteristic values, we are confronted with two problems.

Second, even if the characteristic polynomial factors completely over F into a product of polynomials of degree 1, there may not be enough characteristic vectors for T to span the space V.

This is clearly a deficiency in T.

The second situation is illustrated by the operator T on Af ( F any field ) represented in the standard basis by Af.

The characteristic polynomial for A is Af and this is plainly also the minimal polynomial for A ( or for T ).

Thus T is not diagonalizable.

If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

( C ) if Af is the operator induced on Af by T, then the minimal polynomial for Af is Af.

It is certainly clear that the subspaces Af are invariant under T.

If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

Father Murray goes back to the Declaration of Independence, too, though I may add, with considerably more historical perception.

The same month that Alastor was published, Murray sold twenty thousand copies of The Siege Of Corinth, a slovenly bit of Byronism that even Shelley's generosity rebelled at.

Secret Grand Jury indictments were returned against the pair last week, Detective Murray Logan reported.

The Murray Co. of Texas, Inc., originated in Dallas in 1896.

Murray makes a complete line of ginning equipment except for driers and cleaners, and this machinery is purchased from a Dallas-based firm.

pianists Leon Fleisher, Ruth Slenczynka and Stephen Bishop and conductor Earl Bernard Murray.

Murray Louis and his dance company appeared at the Henry Street Playhouse on Friday and Saturday evenings and Sunday afternoons in the premiere of his latest work, `` Signal '', and the repetition of an earlier one, `` Journal ''.

* Murray, E. ( 1950 ).

London: J. Murray.

* 1919 – Murray Grand, American singer-songwriter and pianist ( d. 2007 )

Murray Rothbard said that the difference between free-market capitalism and " state capitalism " is the difference between " peaceful, voluntary exchange " and a collusive partnership between business and government that uses coercion to subvert the free market.

Anarchist theorist Murray Rothbard argued that all government services, including defense, are inefficient because they lack a market-based pricing mechanism regulated by the voluntary decisions of consumers purchasing services that fulfill their highest-priority needs and by investors seeking the most profitable enterprises to invest in.

* Man, Economy, and State by Murray N. Rothbard

Trade links with the rest of the Australian states were established with the Murray River being successfully navigated in 1853 by Francis Cadell, an Adelaide resident.

* The Abduction ( novel ), 1987, also called Bortførelsen, written in Norwegian by Mette Newth, translated into English by Steven T. Murray and Tiina Nunnally

* Wolf Music: Tapio for Alphorn and echoing Instruments ( 2003 ) by R. Murray Schafer

The Iliad with an English Translation by A. T. Murray, Ph. D. in two volumes.

* 1862 – Nicholas Murray Butler, American philosopher, diplomat, and educator, recipient of the Nobel Peace Prize ( d. 1947 )

* 1916 – World War I: Battle of Romani – Allied forces, under the command of Archibald Murray, defeat an attacking Ottoman army under the command of Friedrich Freiherr Kress von Kressenstein, securing the Suez Canal and beginning the Ottoman retreat from the Sinai Peninsula.

The Ásatrú Alliance is the oldest surviving organization and is headed by Valgard Murray.