Robert Carradine's death has been officially ruled a suicide, and he took his own life by hanging ... according to the Los Angeles County Medical Examiner.

The actor's manner of death is listed as suicide and the cause of death is sequelae of anoxic brain injury and hanging. In other words, he died from a lack of oxygen to the brain.

We learned earlier today Robert died in a hospital in L.A. ... and these details arrive just days after his family announced his death by suicide Monday. They revealed he'd been battling bipolar depression for decades prior to his death.

His family's been very open about Robert's struggle with bipolar disorder ... telling fans they want everyone to know there's no shame in the illness his brother Keith says "got the best of him."

Carradine appeared in popular flicks like "Mean Streets" and "Coming Home" before garnering national recognition for playing Lewis Skolnick in "Revenge of the Nerds."

Younger audiences will recognize him as Lizzie McGuire's dad in 65 episodes of the hit TV show ... as well as "The Lizzie McGuire Movie" in 2003.
Robert was 71.

REST IN PEACE MR. CARRADINE.