The difference between Norm and Normalize

When used as verbs, norm means to endow (a vector space, etc) with a norm, whereas normalize means to make normal, to make standard.

Norm is also noun with the meaning: that which is regarded as normal or typical.

check bellow for the other definitions of Norm and Normalize

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."
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."
Norm as a noun (philosophy, computer science):

A sentence with non-descriptive meaning, such as a command, permission or prohibition.
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).
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.

Norm as a verb (analysis):

To endow (a vector space, etc) with a norm.

Normalize as a verb (transitive):

To make normal, to make standard.

Examples:

"There is little hope that the two countries will normalize relations; their governments seem to hate each other and would just as soon stay on bad terms."
Normalize as a verb (transitive):

To format in a standardized manner, to make consistent.

Examples:

"We'll need to normalize these statements before we can compare them."
Normalize as a verb (transitive, statistics):

To reduce to variations by excluding irrelevant aspects.

Examples:

"After we properly normalize the measurements with respect to age, gender, geography and economic considerations, there remains little evidence of a difference between the two groups."
Normalize as a verb (rail transport, transitive):

To return a set of points (switches) to the normal position.
Normalize as a verb (rail transport, intransitive, of points):

To return to the normal position from the reverse position.
Normalize as a verb (transitive, computing, database):

To subject to normalization; to eliminate redundancy in (a model for storing data).
Normalize as a verb (transitive, mathematics):

To divide a vector by its magnitude to produce a unit vector.