Bhagavad-Gita: Chapter 10, Verse 15

Rudra Vaisnava Sampradaya:

Visnuswami

Sridhara Swami's Commentary

So it is clear that only the Supreme Lord Krishna can know Himself, only by Himself and no one else and nothing else is capable. Out of venerable and great reverence Arjuna addresses Lord Krishna with vocative epithets such as purusottama the greatest personality, bhutesa the Lord of all beings, deva-deva the God of Gods, jagat-pate the Lord of the universe protector of all the worlds.

Brahma Vaisnava Sampradaya:

Madhvacarya
There is no commentary for this verse.

Sri Vaisnava Sampradaya:

Ramanuja

Ramanuja's Commentary

Lord Krishna is being addressed here as Purusottama meaning the Supreme Personality and it is being confirmed that only He can be cognisant of His own Self by His own knowledge and none other. The words bhuta-bhavana means universal father denoting the progenitor of all beings. The word bhutesa means the Lord of all beings indicating the absolute controller. The words jagat-pate refers to Jagannatha the Lord and master of creation. The words deva-deva means God of gods and instructs that even as the demigods excel in innumerable auspicious qualities of form, beauty, aesthetics, etc. over lower and lower creations such as human, animal, birds and reptiles. In the same way the Supreme Lord excels over all of the demigods and any other conceivable god as well.

Kumara Vaisnava Sampradaya:

Nimbaditya

Kesava Kasmiri's Commentary

O' Purusottama meaning the Supreme personality is being used to address Lord Krishna in the vocative case and is being elaborated further by four additional epithets describing His ultimate position as progenitor of all beings, Lord of all beings, Lord of lords and Lord of the universe. In conclusion it is stated that only the Supreme Lord knows Himself by the power of His Self and none else.