MathAlgebraLinear algebraVectors and vector spaces

Vector norm and distance between vectors

Proper metric

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Which of the following must be true for a valid metric:

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d(x,y)=d(y,x)

d(x,y)\geq d(x,z)+d(z,y)

d(x,y)\leq d(x,z)+d(z,y)

d(x,y)=-d(y,x)

d(x,y)=0\Leftrightarrow x=y

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