So from what I've been reading and thinking, a description of an alpha male in general is:

The leader of the pack.
He is a person who gives off a charisma and his actions and words give a direct influence on the people around him.

He is not the one sitting back in a group while somebody is leading a conversation; he is or his presence gives the idea that he is the one fit to lead the group. He knows how to start a conversation and when he does, people listen to him. Even those in the group who were talking separately can't help but to listen when he speaks, because he is interesting.

Sometimes, he may commit actions that seems to be out of the norm. However, thanks to his confidence and natural vibe, it seems to be completely normal and not awkward. For example, he might bring up or make sexual references in a group of many people, which is something that is generally frowned upon. But his skills in conversation and confidence will make it seem like it doesn't matter. It seems that he is the one who defines right and wrong, and normal and weird.

The alpha male is the leader, whom people have respect for and trust. He is alpha not only when he is picking up women but also in his daily life and does not have to "fake it until he becomes it," as he is what he is.

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Is this about right?

For me, this is the exactly the definition of an alpha male.

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Sorry for my english mistakes.