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Webster 1913 Edition

Noun.

Madam; my lady; – a colloquial contraction of madam often used in direct address, and sometimes as an appellation.

Syn. – dame, madam, madame, lady, gentlewoman.

ma'am ‎(plural ma'ams)

In British English, ma'am has become uncommon, although it must be used when addressing the queen more than once: after first addressing her as Your Majesty, one uses ma'am. The term is also sometimes still used in the armed forces and security services when addressing female superiors. Both ma'am and its full form madam are only rarely (far less commonly than in the US) used to express respect outside of these circumstances.
In American English, the full form madam is limited as a form of address to certain highly formal environments, while ma'am is the usual term. Ma'am is not often used in the other sense of madam, but as used as a polite form of address toward (for example, but not strictly limited to):

a female stranger presumed old enough to have children, particularly if older than the speaker,

a female customer one is serving,

one's mother,

a female teacher or school official in a school which emphasizes formality, or

a female superior in the military.

In the southern and southwestern US, ma'am is used to address any female, regardless of her age or position.
South African Usage mirrors American English usage except that ma'am is not used to address one's mother.
In India, ma'am is used to address teachers.
The usage of yes, ma’am connotes deference, particularly by one who has been scolded for misbehavior, but also in more friendly circumstances.

ma'am ‎(third-person singular simple present ma'ams, present participle ma'aming, simple past and past participle ma'amed)

To address (someone) using "ma'am".
- 2013, Debra Clopton, Her Unexpected Cowboy (ISBN 1460324595):
  "Y'all have about ma'amed me to death. But you can call me Lucy from here on out. Got it?” “Yes, ma'am—I mean, Lucy,”