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# Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold.
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# and Any
# Any sufficiently advanced technology is indistinguishable from magic.
# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.
# Any experience which is inconsistent with the organization of the structure of the self may be perceived as a threat, and the more of these perceptions there are, the more rigidly the self structure is organized to maintain itself.
# Any real number can be added to both sides.
# Any real number can be subtracted from both sides.
# Any real number can be multiplied to both sides.
# Any non-zero real number can divide both sides.
# Disturbed natural forest – Any forest type above that has in its interior significant areas of disturbance by people, including clearing, felling for wood extraction, anthropogenic fires, road construction, etc.
# Disturbed natural forest – Any forest type above that has in its interior significant areas of disturbance by people, including clearing, felling for wood extraction, anthropogenic fires, road construction, etc.
# Any two points can be joined by a straight line.
# Any finite straight line can be extended in a straight line.
# Any player qualifying from the Interzonal tournament to play in the Candidates Tournament, even if he did not play in the Candidates for any reason.
# Any player who would qualify from the Interzonal to play in the Candidates but who was excluded because of a limitation on the number of participants from his Federation.
# Any player who actually plays in a Candidates Tournament and scores at least percent.
# Any committee may start a project.
# Any true image of Jesus must be able to represent both his divine nature ( which is impossible because it cannot be seen nor encompassed ) as well his human nature.
Brown continued releasing recordings: in 1993, he issued the album, Universal James, which included Brown's final Billboard charted single, " Can't Get Any Harder ", which peaked at # 76 on the US R & B chart and # 59 on the UK chart.
# Any neighbourhood N of x contains a neighbourhood M of x such that N is a neighbourhood of each point of M.
# Any live cell with fewer than two live neighbours dies, as if caused by under-population.
# Any live cell with two or three live neighbours lives on to the next generation.
# Any live cell with more than three live neighbours dies, as if by overcrowding.
# Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
# Any pure element ( even if it forms diatomic molecules like chlorine, Cl < sub > 2 </ sub >) has an oxidation state ( OS ) of zero.
# and tangent
# Five-pointed star is inscribed into a circle with a diameter of ⅛ of the flag height, the circle is tangent to the upper side of the square.
# REDIRECT tangent # Tangent line to a curve
# as a percentage, the formula for which is which could also be expressed as the tangent of the angle of inclination times 100.
# as a per mille figure, the formula for which is which could also be expressed as the tangent of the angle of inclination times 1000.
The force line ( or gear # Line of Action | Line of Action ) runs along a tangent common to both base circles.
# for all p in P, the restriction of η defines a linear isomorphism from the tangent space T < sub > p </ sub > P to.
Let M be a differentiable manifold and p a point of M. Suppose that f is a function defined in a neighborhood of p, and differentiable at p. If v is a tangent vector to M at p, then the directional derivative of f along v, denoted variously as ( see covariant derivative ), ( see Lie derivative ), or ( see Tangent space # Definition via derivations ), can be defined as follows.
# If there is an irreducible hermitian symmetric space of the form G /( U ( 1 ) · K ), then both H and C *· H are non-symmetric irreducible affine holonomy groups, where V the tangent representation of K.
# M is geodesically complete ; that is, for every p in M, the exponential map exp < sub > p </ sub > is defined on the entire tangent space T < sub > p </ sub > M.
# The envelope E < sub > 2 </ sub > is a curve tangent to all of the C < sub > t </ sub >.
# Arc-Quadrant Systems: Probes are directed perpendicular to the tangent of an arc ( which rotates about the vertical axis ) and a quadrant ( which rotates about the horizontal axis ).
# At each switch, three curves meet with the same tangent line, with two curves entering from one direction and one from the other.
# A North Line from the tangent point to a line running 15 miles south of Philadelphia ( approximately 39 ° 43 ' N latitude ).
# REDIRECT tangent bundle
# REDIRECT tangent
# a nondegenerate 2-form ω which preserves J and is positive-definite in the sense that ω ( u, Ju ) > 0 for all nonzero real tangent vectors u.
# and vector
# If G is any group acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket and therefore also forms a Lie algebra.
# REDIRECT dimension ( vector space )
# Multivariate regression analysis attempts to determine a formula that can describe how elements in a vector of variables respond simultaneously to changes in others.
# The vector addition +: V × V → V is jointly continuous with respect to this topology.
# If n = 2k + 1, then the action of the unit vector u on the left ideal decomposes the space into a pair of isomorphic irreducible eigenspaces ( both denoted by Δ ), corresponding to the respective eigenvalues + 1 and − 1.
# REDIRECT dimension ( vector space )
Right: The reduction in flux passing through a surface can be visualized by reduction in F or dS equivalently ( resolved into Euclidean vector # Decomposition | components, θ is angle to normal n ).
# Move the nearest quantization vector centroid towards this sample point, by a small fraction of the distance
# Find the quantization vector centroid with the smallest < distance-sensitivity >
# The zero vector, 0, is in W.
# REDIRECT vector processor
# REDIRECT vector processor
# Null ( A ) always contains the zero vector, since A0 = 0.
# Grab an input vector
# Update the nodes in the neighborhood of the BMU ( including the BMU itself ) by pulling them closer to the input vector
# REDIRECT Support vector machine
# The vector v can be interpreted as a rank 1 tensor with dimension M, and the vector u as a rank 1 tensor with dimension N. The result is a rank 2 tensor with dimension ( M, N ).
# The cross product is left-and right-distributive over vector addition, though not commutative.
# REDIRECT dimension ( vector space )
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