Link to purport by A C Bhaktivedanta Swami Srila Prabhupada

Transcript of Bhakti-Shastri class on this verse by Chaitanya Charan

10.19 was introductory verse.

Bg 10.20

aham ātmā guḍākeśa
sarva-bhūtāśaya-sthitaḥ
aham ādiś ca madhyaṁ ca
bhūtānām anta eva ca

Word for word: 

aham — I; ātmā — the soul; guḍākeśa — O Arjuna; sarva–bhūta — of all living entities; āśaya–sthitaḥ — situated within the heart; aham — I am; ādiḥ — the origin; ca — also; madhyam — middle; ca — also; bhūtānām — of all living entities; antaḥ — end; eva — certainly; ca — and.

Translation: 

I am the Supersoul, O Arjuna, seated in the hearts of all living entities. I am the beginning, the middle and the end of all beings.

aham ātmā guḍākeśa, so Arjuna is referred as guḍākeśa, who has conquered the sleep other meaning is one who gives sweetness to Lord Brahma and Shiva. This is possible when devotees has love and devotion Lord always have love towards us. 

aham ātmā, I am the atma

sarva-bhūtāśaya-sthitaḥ, who is situated in all living entities sarva-bhūtāśaya

So is this means Mayavad that it is same soul which is situated in every living beings? No Krishna has already said soul can never be cut so it is distinct soul and not cut from another soul, and that souls goes from one body to another body so it is not that same soul is present in all the bodies in that case how it will go from one body to another body? 

So atma refers to Super Soul here, so here Krishna describes how He pervades space and time, space – in heart of all living being.

aham ādiś ca madhyaṁ ca
bhūtānām anta eva ca

I am the beginning, middle and end, beginning Maha-Vishnu, in middle we are not maintaining but He is maintaining, food digestion, air circulation in body etc.  Ultimately Krishna is saying I am death. Also all souls enters in Maha-vishnu at the time of annihilation.

This can also refer to as Brahma, Vishnu and Mahesh who are Guna Avatara.

End of transcription.