No, triggers are object specific at the moment. If you want, you can vote on an existing idea. Additionally, in the apex triggers best practices guide, you can read additional details (further developing and adding more details)

No, triggers are object specific, you can see, the first line of code gives the trigger a name, specifies the object on which it operates, and defines the events that cause it to fire:

trigger TriggerName on ObjectName (trigger_events) {
   code_block
}

If you want, you can vote on an existing idea for supporting multiple objects. 

Additionally, in the apex triggers best practices guide, you can read further details details on trigger best practices.