B.G 4.05 and 06

श्रीभगवानुवाच
बहूनि मे व्यतीतानि जन्मानि तव चार्जुन। तान्यहं वेद सर्वाणि न त्वं वेत्थ परन्तप ॥५॥

śrībhagavānuvāca
bahūni mē vyatītāni janmāni tava cārjuna। tānyahaṁ vēda sarvāṇi na tvaṁ vēttha parantapa ॥5॥

The Supreme Lord said:
O Arjuna, you and I have passed through many lives. I know all of them, but you, O Subduer of enemies, are not acquainted with them.

अजोऽपि सन्नव्ययात्मा भूतानामीश्वरोऽपि सन्। प्रकृतिं स्वामधिष्ठाय सम्भवाम्यात्ममायया ॥६॥

ajō'pi sannavyayātmā bhūtānāmīśvarō'pi san। prakr̥tiṁ svāmadhiṣṭhāya sambhavāmyātmamāyayā ॥6॥

Though my body is imperishable and I am the supreme lord of all the beings, I re-manifest and seem to be born, having established myself in my own inherent nature with the delusional power I possess.

Gīta Bhāshya 4.05 and 06

'avyayātmā' - the body of the lord is imperishable. 'ātmamāyayā' - knowledge of the 'ātman' / power of mine. 'Īsvara' - primarily refers to lord Vishnu as he is the lord of other lords as well. Grasping the omnipotent quality of the divine resolves the conflict of Him embodying both the principle and the personality.

How then are you stated to be without beginning? - is answered by 'ajo' verse.

The word 'avyayātmā', i.e. imperishable being, is used, as the body of the lord is also imperishable.

"He is infinite, having the universe as the face." (11.11)

This indeed, is the answer given (in 11.11) to describe the special form of the lord.

"This (lord) is the source and indestructible seed of various incarnations."

-stated thus, as well, in the testimonial (Bhagavata 1.3.5).

The expression "he took hold" ('jagr̥hē' used in 1.3.1 of Bhagavata) indicates Him to be a personality. The solution to resolve (the dual aspect of lord being both a pinciple as well as personality) is already explained (in 2nd chapter, by noting that he is all powerful). The 'ātmān' is equal in all. How is He born, though is eternal and without beginning? Having established Himself in his inherent nature, i.e. 'prakrti'. His inherent nature manifests from the forms of the lord such as Vasudeva etc. Therefore it is understood - "She (prakrti) seems to appear as if born". Indeed, She does not independently establish herself, hence it is said - 'svām', i.e. "by my own".

"Substances and actions as well."

-stated thus by testimonials.

Indeed, She (prakrti) is described thus (, and so is dependent). Same is true with the whole of creation as well.

The word 'ātmamāyayā' means by the knowledge of the 'ātman', i.e. knowledge of the Lord. It is not referring to 'Prakrti' as it is already distinctly identified (by 'prakrti' word).

The words 'kētuḥ', 'kētah', 'chitti', 'chittam', 'matihi', 'kratuh', 'manisha', and 'māya' are said to convey the same meaning as per thesaurus.

Or, For the purpose of creation, though he is unborn, through His deluding power, he appears as if to possess a physical body and other attributes like normal being. Therefore, it is said:

"She who is mother of ego and other principles is conceived by the name 'Shri', 'Bhoo" etc. Her deluding power is known by the name 'Durga'. Lord Vishnu, though unborn through Her, the insentient, appears as born to the deluded, by His own energy."

-states testimonial.

The word 'Īsvara' means, He is superior to all other owners. Therefore, it is said:

"You are superior compared to other lords like Shri, Brahma, Rudra, Shesha and others. Thus the title 'Īsvara' is primarily yours and not for others at any point in time."

-states Brahma Vaivarta Purana.

"The capable is called 'Īsha'; You are called 'Īsvara' as you are even superior to them."

-is also the testimonial.