The difference between Absolute value and Norm
When used as nouns, absolute value means for a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, \sqrt{a^2+b^2}. denoted by | |, whereas norm means that which is regarded as normal or typical.
Norm is also verb with the meaning: to endow (a vector space, etc) with a norm.
check bellow for the other definitions of Absolute value and Norm
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Absolute value as a noun (mathematics):
For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, \sqrt{a^2+b^2}. Denoted by | |.
Examples:
"The absolute value x of a real number x is <math>\sqrt{x^2}</math>, which is equal to x if x is non-negative, and −x if x is negative."
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Norm as a noun (usually, definite, '''the norm'''):
That which is regarded as normal or typical.
Examples:
"Unemployment is the norm in this part of the country."
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Norm as a noun:
A rule that is enforced by members of a community.
Examples:
"Not eating your children is just one of those societal norms."
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Norm as a noun (philosophy, computer science):
A sentence with non-descriptive meaning, such as a command, permission or prohibition.
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Norm as a noun (mathematics):
A function, generally denoted v\mapsto\left|v\right| or v\mapsto\left\|v\right\|, that maps vectors to non-negative scalars and has the following properties: if v\ne0 then \left\|v\right\|\ne0; given a scalar k, \left\|kv\right\|=\left|k\right|\cdot\left\|v\right\|, where \left|k\right| is the absolute value of k; given two vectors v,w, \left\|v+w\right\|\le\left\|v\right\|+\left\|w\right\| (the triangle inequality).
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Norm as a noun (chess):
A high level of performance in a chess tournament, several of which are required for a player to receive a title.
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Norm as a verb (analysis):
To endow (a vector space, etc) with a norm.