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https://en.wikipedia.org/wiki/Linear_combinations
The subtle difference between these uses is the essence of the notion of linear dependence: a family F of vectors is linearly independent precisely if any linear combination of the vectors in F (as value) is uniquely so (as expression)
https://en.wikipedia.org/wiki/Euclidean_geometry
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https://en.wikipedia.org/wiki/Pauli_principle
For example, if two electrons reside in the same orbital, then their values of n, ℓ, and mℓ are equal
https://en.wikipedia.org/wiki/Palestinian_Prisoners'_Document
or at least [imply] acceptance of Israel if it withdraws to its 1967 borders",[4] such recognition of "Israel's right to exist in peace and security" being one of the key demands of the road map for peace
https://en.wikipedia.org/wiki/Social_inequality
[1]
Social inequality is linked to economic inequality, usually described as the basis of the unequal distribution of income or wealth
https://en.wikipedia.org/wiki/Dot_product
to an orthonormal basis, is defined, in summation notation, as:[2]
a ⋅ b = ∑ i = 1 n a i b i = a 1 b 1 + a 2 b 2 + ⋯ + a n b n {\displaystyle \mathbf {a} \cdot \mathbf {b} =\sum _{i=1}^{n}a_{i}b_{i}=a_{1}b_{1}+a_{2}b_{2}+\cdots +a_{n}b_{n}}
where n {\displaystyle n} is the dimension of the vector space
https://en.wikipedia.org/wiki/Linear_differential_equation
A linear differential equation may also be a linear partial differential equation (PDE), if the unknown function depends on several variables, and the derivatives that appear in the equation are partial derivatives
https://en.wikipedia.org/wiki/Linear_map
A function f : V → W {\displaystyle f:V\to W} is said to be a linear map if for any two vectors u , v ∈ V {\textstyle \mathbf {u} ,\mathbf {v} \in V} and any scalar c ∈ K {\displaystyle c\in K} the following two conditions are satisfied:
Additivity / operation of addition[note 2] f ( u + v ) = f ( u ) + f ( v )
https://en.wikipedia.org/wiki/Euclidean_space
One of the basic tenets of Euclidean geometry is that two figures (usually considered as subsets) of the plane should be considered equivalent (congruent) if one can be transformed into the other by some sequence of translations, rotations and reflections (see below)
https://en.wikipedia.org/wiki/Minority_government
A minority government tends to be less stable than a majority government because, if they can unite, opposing parliamentary members have sufficient numbers to vote against legislation, or even bring down the government with a vote of no confidence
https://en.wikipedia.org/wiki/Donoghue_v_Stevenson
html [1930] SN 138])<ref name=\"Mrs Donoghue's Journey\" />"},"opinions":{"wt":"Manufacturers have a legal duty of care to the ultimate consumers of their products if it is not possible for defects to be identified before the goods are received
https://en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field
If only the electric field (E) is non-zero, and is constant in time, the field is said to be an electrostatic field
https://en.wikipedia.org/wiki/Insanity_defense
Being incapable of distinguishing right from wrong is one basis for being found to be legally insane as a criminal defense
https://en.wikipedia.org/wiki/Affine_space
However, if the sum of the coefficients in a linear combination is 1, then Alice and Bob will arrive at the same answer
https://en.wikipedia.org/wiki/Algebraic_geometry
A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation
https://en.wikipedia.org/wiki/Presidential_eligibility_of_Donald_Trump
Constitution, which disqualifies insurrectionists against the United States from holding office if they have previously taken an oath to support the constitution
https://en.wikipedia.org/wiki/Wavelet
If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the middle C note appeared in the song
https://en.wikipedia.org/wiki/Waste_management_in_Australia
[3] Sydney Harbour was the major dumping site
https://en.wikipedia.org/wiki/Affine_connection
In differential geometry, an affine connection[a] is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space
https://en.wikipedia.org/wiki/Legal_status_of_transgender_people
Not all transgender or transsexual people feel gender dysphoria or gender incongruence, but in many countries a diagnosis is required for legal recognition, if transgender people are legally recognized at all
https://en.wikipedia.org/wiki/Geographia
[18]
Regarding the maps, they conclude that it was unlikely that extant maps survived from which the above stemma descends, even if maps existed in antiquity:
"Th
https://en.wikipedia.org/wiki/Jeremy_Thorpe
He was offered a cabinet post by the Conservative prime minister, Edward Heath, if he would bring the Liberals into a coalition government
https://en.wikipedia.org/wiki/Waters_v._Churchill
They vacated a Seventh Circuit Court of Appeals ruling in her favor, and ordered the case remanded to district court to determine instead if the nurse had been fired for the speech or other reasons, per the Court's ruling two decades prior in Mt
https://en.wikipedia.org/wiki/Moment_magnitude_scale
)
The local magnitude scale was developed on the basis of shallow (~15 km (9 mi) deep), moderate-sized earthquakes at a distance of approximately 100 to 600 km (62 to 373 mi), conditions where the surface waves are predominant
https://en.wikipedia.org/wiki/Oliver_Wendell_Holmes_Jr.
Emerson famously replied, "If you strike at a king, you must kill him
https://en.wikipedia.org/wiki/Freedom_suit
Petitioners challenged slavery both directly and indirectly, even if slaveholders generally viewed such petitions as a means to uphold rather than undermine slavery
https://en.wikipedia.org/wiki/Alcohol_tax
See Wikipedia's guide to writing better articles for suggestions
https://en.wikipedia.org/wiki/Climate_change_in_the_Arctic
If the warming exceeds - or thereabouts, there is a significant risk of the entire ice sheet being lost over an estimated 10,000 years, adding up to global sea levels
https://en.wikipedia.org/wiki/Constitution
supreme law, is the aggregate of fundamental principles or established precedents that constitute the legal basis of a polity, organization or other type of entity, and commonly determines how that entity is to be governed
https://en.wikipedia.org/wiki/International_Court_of_Justice
-- year term of current chief ends if applicable -->"},"chiefjudgetitle2":{"wt":"Vice President"},"chiefjudgename2":{"wt":"[[Julia Sebutinde]]"},"termstart2":{"wt":"6 February 2024"},"termend3":{"wt":""},"termend4":{"wt":