How to pronounce “two-norm”

Meaning

• [Noun]
• (mathematics) A measure of length given by "the square root of the squares." Denoted by
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• ⋅
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• 2
• {\displaystyle ||\cdot ||_{2}}
• , the two-norm of a vector
• v
• →
• =<
• a
• 1
• ,
• a
• 2
• ,
• …
• ,
• a
• n
• >
• {\displaystyle {\vec {v}}=<a_{1},a_{2},\ldots ,a_{n}>}
• is
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• v
• →
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• |
• 2
• =
• a
• 1
• 2
• +
• a
• 2
• 2
• +
• ⋯
• +
• a
• n
• 2
• {\displaystyle ||{\vec {v}}||_{2}={\sqrt {a_{1}^{2}+a_{2}^{2}+\cdots +a_{n}^{2}}}}
• . The two norm of an
• m
• ×
• m
• {\displaystyle m\times m}
• matrix
• A
• {\displaystyle A}
• is defined by
• max
• v
• →
• ≠
• 0
• →
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• A
• v
• →
• |
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• 2
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• v
• →
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• 2
• {\displaystyle \max _{{\vec {v}}\neq {\vec {0}}}{\frac {||A{\vec {v}}||_{2}}{||{\vec {v}}||_{2}}}}
• where
• v
• →
• {\displaystyle {\vec {v}}}
• is an m-dimensional vector that is not the zero vector.

Practice Nearby Words

magnitude, norm, conorm, normed vector space, semi-norm, norming, euclidean norm, seminorm, metanorm, normaloid, gauge, renorming, t-norm, normality, mean square, quasinorm, tensor, unit vector, orthonormalisation, root mean square, orthogonal matrix, orthonormalization, square, difference of two squares, n-dimensional space, trivial absolute value, dual, mean, square root, quadratic mean, orthonormality, vector function, contraharmonic mean, gowers norm, biset, two-form, sobolev space, geometric mean, p-adic norm, dimension, euclidean metric, orthonormal function, triangle inequality, geometric multiplicity, minkowski inequality, metric, bilinear form, measure, versor, absolute value, t-conorm, nonsquare, heterosquare, euclidean space, row vector, vector, metric tensor, bicoherence, area, distance formula, dyad, semilength, nullity, binary function, uniform metric, normal form, supersquare, dual space, bivector, multivector, duotensor, biordinal, involutant, valuation, vector product, natural number, codimension, row space, rank, autometry, even number, binary logarithm, orientation, nonhypotenuse number, eigenorder, scalar multiplication, inverse matrix, newton number, covariance, non-hypotenuse number, column vector, quadratic form, cauchy-schwarz inequality, modulus, standard normal distribution, dual number, scalar product, orthogonal function, arithmetic-geometric mean

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