Talk to him is what I did

Talk to him is what I did.

(this sentence is from forum.wordreference.com)

"Talk" is a verb here that is not in the imperative mood. I suppose, it's in the infinitive form. But then how can it stand alone, without "to"?

What will be if we add "to" to "talk"?

To talk to him is what I did.

If we can do so, then what will difference be between the initial sentence and the new one with "to"?

Maybe, there are some omitted words, after inserting which the sentence will immediately become understandable? I mean, maybe, there is an ellipsis?

Thanks!

To make it clearer:

Upd.1: if we type "bare infinitive" in google, we can't find any sites that could explain the absence from "to" before "talk".

Upd.2: Why can we replace "to talk" with only "talk" in "To talk to him is what I did."

Upd.3: I have my own logic but I don't know whether it's right or not:

1) I think that without an ellipsis "Talk to him is what I did." is to look like "I did talk to him is what I did do."

2) Also I know that we can't use "to" before "read" in "What we must do is read the manual." because in the left part we don't have "to" before "do".

By this logic, we can't use "to" before "talk" in "Talk to him is what I did." because in "what I did do" we don't have "to" before "do".

Am I right or not?

Solution 1:

The regular order here is:

• What I did was talk to him.
• What I did is talk to him.
• What I saw was a lion in the tree.
• How he came was by bus.
• What we did was complain a lot.
• What I did was talk.

Now, when the verb is BE, you can invert the noun phrases on either side of it. Think of the verb was here as an equals' sign. All of the examples above can be reworded.

• Talk to him was what I did.
• Talk to him is what I did.
• A lion in the tree is what I saw.
• By bus was how he came.
• Complain a lot was what we did.
• Talk was what I did.

The verb be can be in the present or past. The second noun phrase can be placed in initial position. This type of style change is used for emphasis.

If you say "Talk to him was what I did", the talking is more important to you than the doing as in "What I did was talk to him". So, which form you use depends on what you want to stress.

This is called copular inversion.

EDIT: Any action verb can be used in these inversions. It is not necessary to use "talk to him". Just talk on its own can be used.

copular inversion