The determinant provides important information when the matrix is that of the coefficients of a system of linear equations, or when it corresponds to a linear transformation of a vector space: in the first case the system has a unique solution if and only if the determinant is nonzero, while in the second case that same condition means that the transformation has an inverse operation.

Emperor Theodosius I permits Alaric to go free on condition he provides, as foederati, military services to the Roman Empire.

Hempel's equivalence condition states that when a proposition, X, provides evidence in favor of another proposition Y, then X also provides evidence in favor of any proposition which is logically equivalent to Y.

The sampling theorem provides a sufficient condition, but not a necessary one, for perfect reconstruction.

The field of compressed sensing provides a stricter sampling condition when the underlying signal is known to be sparse.

This condition is known as Sylvester's criterion, and provides an efficient test of positive-definiteness of a symmetric real matrix.

Many types of component use electronic sensors to capture data which provides live condition monitoring.

) It requires less frequent synchronization than the earlier superframe or D-4 format, and provides on-line, real-time testing of circuit capability and operating condition.

The differential equation, with the inclusion of a boundary condition providing a third degree of freedom,, provides a class of functions of this type.

A charter change in 1995 led by the receivership through a community process designed an efficient council-manager form of government, which has focused on improving the quality of service the city provides to its residents and businesses, while establishing financial policies that have significantly improved the city's financial condition.

In England the Single Payment Scheme provides a single flat rate payment of around £ 230 per hectare for maintaining land in cultivatable condition.

This property provides a simple method to test the condition of orthogonality.

The Code of Canon Law provides: " A marriage subject to a condition about the future cannot be contracted validly.

Some don't mind preaching but are concerned if the speech is accompanied by material benefits ( e. g., a soup kitchen that provides food, but only under the condition that the recipients listen to an evangelical discourse ) or new converts are given material benefits not available to those who don't convert.

The museum is a rich response to Melbourne ’ s urban condition, and provides a place for education, history, culture and society to engage with each other in a contemporary setting.

The implicit function theorem provides a condition under which a relation defines an implicit function.

When the barrier field F is high enough for the CFE regime to be operating for metal emission at 0 K, then the condition k < sub > B </ sub > T < d < sub > F </ sub > provides a formal upper bound ( in temperature ) to the CFE emission regime.

In cases where local analysis ( plus the condition that there are real solutions ) provides also sufficient conditions, one says that the Hasse principle holds: this is the best possible situation.

The theorem may be interpreted to saying that a holomorphic function satisfying certain growth condition is necessarily algebraic: " projective " provides this growth condition.

In the theory of formal languages, the Myhill – Nerode theorem provides a necessary and sufficient condition for a language to be regular.

This condition provides more liberty for the courts to respond with an appropriate sentence to serious offences.

According to one paradigm, the leading edge of a gravity current ' controls ' the flow behind it: it provides a boundary condition for the flow.

: A practical issue is whether the fact that an accused is labouring under a " mental disability " should be a necessary but not sufficient condition for negating responsibility i. e. whether the test should also require an incapacity to understand what is being done, to know that what one is doing is wrong, or to control an impulse to do something and so demonstrate a causal link between the disability and the potentially criminal acts and omissions.

Note: during the on-hook condition, the link is responsive to ringing signals.

The first condition can be satisfied by comparing metrics from all neighboring routers that advertise that particular destination, increasing the metrics by the cost of the link to that respective neighbor, and selecting the neighbor that yields the least total distance.

Experts note that because of the possible link of akathisia with suicide and the distress it causes to the patient, " it is of vital importance to increase awareness amongst staff and patients of the symptoms of this relatively common condition ".

The extra condition which was needed to link Taniyama-Shimura-Weil to Fermat's Last Theorem was identified by and became known as the epsilon conjecture.

Drop the PDU and send an Internet Control Message Protocol ( ICMP ) message which indicates the condition Packet too Big, or to fragment the IP packet and send it over the link with a smaller MTU.

The proposed condition PANDAS ( pediatric autoimmune neuropsychiatric disorders associated with streptococcal infections ) has been used to describe a set of children who have a rapid onset of OCD and / or tic disorders following a streptococcal infection, with a link to other symptoms such as enuresis.

These cognitions of impending death with retraction and perceived spermatorrhea has a strong cultural link with Chinese traditional beliefs, as demonstrated by the fact that in general, Asians with complaints of genital retraction believe that the condition is fatal, unlike most Westerners.

It is also a major road link for the eastern and western parts of the country to the capital city of Kathmandu ( the highway to Lhasa is blocked by landslides, the Naubise-Hetauda highway is in poor condition and time consuming and a latest road from Dhulikhel to Kamalamai ( Sindhulimadi ) is under construction ).

It will allow researchers to link a given condition to a given gene or set of genes using the LD as a marker.

If there is no link between given nodes, then an error condition is usually triggered with a message such as " Invalid Path ".

However despite the antidote, Mar-Vell still developed cancer and there was some momentary concern that the link Rick shared with him could have caused himself to contract the condition.

A link between stress and this condition has also been shown.

The State Government refused to impose a condition sought by the Stonnington Council calling for a transport study by the Government and Gandel, including the possible construction of a rail link.

While the common name " tennis elbow " suggests a strong link to racquet sports, this condition can also be caused by sports such as swimming and climbing, the work of manual workers and waiters, as well as activities of daily living.

Negotiations subsequently turned towards the amount of that tax, and Switzerland offered to build a new high-speed rail link through the Alps for the main purpose of intermodal transport, an offer which was later accepted by the EU but not without attaching the condition that the then valid 28-tonne limit for trucks must be raised to 48 tonnes.

The Grashof condition for a four-bar linkage states: If the sum of the shortest and longest link of a planar quadrilateral linkage is less than or equal to the sum of the remaining two links, then the shortest link can rotate fully with respect to a neighboring link.

In other words, the condition is satisfied if S + L ≤ P + Q where S is the shortest link, L is the longest, and P and Q are the other links.

The only other paved road, Livingstone in Southern Province to Sesheke and the Katima Mulilo Bridge is in good condition as a result of being upgraded to link to the Trans – Caprivi Highway.

With investments in Earth observations now reaching a critical mass, it has become possible to link diverse observing systems together to paint a full picture of the Earth ’ s condition.

* As a transmitter / studio link, sending telemetry data from a broadcast FM station's transmitter to the studio for monitoring the condition of the transmitter