The Bhagavad Gita with Commentaries of Ramanuja, Madhva, Shankara and Others.
Bhagavad Gita 4.6
http://www.bhagavad-gita.us/articles/501/1/Bhagavad-Gita-46/Page1.html
By Bhagavan Sri Krishna
 

Text 6

 ajo ’pi sann avyayatma
bhutanam isvaro ’pi san
prakritim svam adhisthaya
sambhavamy atma-mayaya

 Translation

Although I am unborn and My transcendental body never deteriorates, and although I am the Lord of all living entities, I still appear in every millennium in My original transcendental form.

Commentary by Srila Prabhupada 

The Lord has spoken about the peculiarity of His birth: although He may appear like an ordinary person, He remembers everything of His many, many past “births,” whereas a common man cannot remember what he has done even a few hours before. If someone is asked what he did exactly at the same time one day earlier, it would be very difficult for a common man to answer immediately. He would surely have to dredge his memory to recall what he was doing exactly at the same time one day before. And yet, men often dare claim to be God, or Krishna. One should not be misled by such meaningless claims. Then again, the Lord explains His prakriti, or His form. Prakriti means “nature,” as well as svarupa, or “one’s own form.” The Lord says that He appears in His own body. He does not change His body, as the common living entity changes from one body to another. The conditioned soul may have one kind of body in the present birth, but he has a different body in the next birth. In the material world, the living entity has no fixed body but transmigrates from one body to another. The Lord, however, does not do so. Whenever He appears, He does so in the same original body, by His internal potency. In other words, Krishna appears in this material world in His original eternal form, with two hands, holding a flute. He appears exactly in His eternal body, uncontaminated by this material world. Although He appears in the same transcendental body and is Lord of the universe, it still appears that He takes His birth like an ordinary living entity. And although His body does not deteriorate like a material body, it still appears that Lord Krishna grows from childhood to boyhood and from boyhood to youth. But astonishingly enough He never ages beyond youth. At the time of the Battle of Kurukshetra, He had many grandchildren at home; or, in other words, He had sufficiently aged by material calculations. Still He looked just like a young man twenty or twenty-five years old. We never see a picture of Krishna in old age because He never grows old like us, although He is the oldest person in the whole creation—past, present, and future. Neither His body nor His intelligence ever deteriorates or changes. Therefore, it is clear that in spite of His being in the material world, He is the same unborn, eternal form of bliss and knowledge, changeless in His transcendental body and intelligence. Factually, His appearance and disappearance is like the sun’s rising, moving before us, and then disappearing from our eyesight. When the sun is out of sight, we think that the sun is set, and when the sun is before our eyes, we think that the sun is on the horizon. Actually, the sun is always in its fixed position, but owing to our defective, insufficient senses, we calculate the appearance and disappearance of the sun in the sky. And because Lord Krishna’s appearance and disappearance are completely different from that of any ordinary, common living entity, it is evident that He is eternal, blissful knowledge by His internal potency—and He is never contaminated by material nature. The Vedas also confirm that the Supreme Personality of Godhead is unborn yet He still appears to take His birth in multimanifestations. The Vedic supplementary literatures also confirm that even though the Lord appears to be taking His birth, He is still without change of body. In the Bhagavatam, He appears before His mother as Narayana, with four hands and the decorations of the six kinds of full opulences. His appearance in His original eternal form is His causeless mercy, bestowed upon the living entities so that they can concentrate on the Supreme Lord as He is, and not on mental concoctions or imaginations, which the impersonalist wrongly thinks the Lord’s forms to be. The word maya, or atma-maya, refers to the Lord’s causeless mercy, according to the Vishva-kosa dictionary. The Lord is conscious of all of His previous appearances and disappearances, but a common living entity forgets everything about his past body as soon as he gets another body. He is the Lord of all living entities because He performs wonderful and superhuman activities while He is on this earth. Therefore, the Lord is always the same Absolute Truth and is without differentiation between His form and self, or between His quality and body. A question may now be raised as to why the Lord appears and disappears in this world. This is explained in the next verse.

Commentary by Sri Visvanatha Cakravarti Thakur

In this verse, he describes the manner of his appearance.

"Though I am without birth, I appear. I descend in the forms of devas, humans and crawling animals and other forms."

"But what is remarkable about that? The jiva is also actually without birth, and is born again after the destruction of the gross body."

The Lord answers: "I have an indestructible body (avyaya atma). The jiva is without birth in the sense that he is a soul apart from his body. He takes birth just because of his relationship with the body which produces ignorance. But my being without birth and my taking birth are not separate from my body, since I am the Lord. Both my birth and not being born are in the same form. As such a thing is difficult to happen, it is certainly astounding and inconceivable. And there is no worry that I will take birth in all sorts of wombs like the jiva who is under the influence of papa and punya, for I am the lord of all the living entities (bhutanam isvarah), not under the control of karma."

"But the jiva receives bodies of deva, human and animal according to karma by his subtle body which causes his bondage. You, the Supreme Lord, are without a subtle body, and you are all pervading and control karma, time and all other elements. The Sruti says bahu syam: may I become many. (Chandogya Upanisad 6.2.3) From that, it is understood that you are the form of the whole universe. When you say 'I appear in this particular way,' I think that must mean that your birth means simply your revealing to people the multitude of varieties of bodies in the whole universe, which are also eternal as types."

"But how can that be? I make my appearance, situated in my own form (prakrtim svam adhisthaya)."

If the word prakrti meant the external material energy, then its controller, the Supreme Lord, becomes, by inference, a material form, not a special object of realization. Therefore, in conformity to the dictionary meaning (samsiddhi-prakrti tv ime svarupam ca svabhavas ca), the word prakrti means svarupa in this verse. It does not refer to the material energy which arises from his svarupa. The Lord's svarupa is sac cid ananda.

Concerning the word prakrti, Sridhara Swami says, "You are prakrti which is composed of suddha sattva." Ramanujacarya. says, "Prakrti means ones own nature. Thus the phrase 'Being situated in my nature,' means 'I appear with my svarupa by my own will.'"

Thus, prakrti means one's nature, which is condensed sac cid ananda rasa, which is distinct from material energy. The word svam along with prakrti thus indicates "my own true form," as distinct from others' true forms.

For the sruti says:

sa bhagavah kasmin pratisthitah sva mahimni

Dear sir, in what is the supreme situated? It is situated in its own glory.  Chandogya Upanisad 7.24.1

Madhusudana Sarasvati gives the following meaning. "I appear, situated in my svarupa. Being situated spiritually, I act without duality of soul and body."

"But if you have indestructible bodies such as Matsya or Kurma, then why do not your present form and the previous forms appear all at once?

"I appear through my maya coming from my self (atma means self, thus atma maya means my own maya), yoga maya, the function of the cit sakti, which both covers and reveals my svarupas. I appear revealing my present form, having covered the previous forms."

Sridhar Swami says, "I appear by my energy of jnana, bala and virya which strongly manifest (atma mayaya)."

Atma mayaya can also mean "By my own knowledge," since maya can mean knowledge in this context: maya vayunam jnanam. The usage is stated by Ramanujacarya: "He continually knows the sin and piety of all entities by knowledge (mayaya)." Madhusadana Sarasvati says: "Maya means the awareness through that body (atma) that I am the Lord, Vasudeva, devoid of difference between body and soul."