In plain words
I am seated in the heart of all; from Me arise memory, jñāna, and the loss of both. I alone am to be known through all the Vedas; I am the founder of the tradition of Vedānta and the knower of the Vedas.
Word for word
And I am seated in the heart of all; from Me [come] memory, knowledge and [their] loss; and by all the Vedas I alone [am] to be known; the maker of the Vedānta and the knower of the Veda indeed am I.
सर्वस्य चाहं हृदि सन्निविष्टोमत्तः स्मृतिर्ज्ञानमपोहनं चवेदैश्च सर्वैरहमेव वेद्योवेदान्तकृद् वेदविदेव चाहम्
Other commentaries
The commentators
▸Bhagavadgītābhāṣyam
किञ्च —
सर्वस्य च प्राणिजातस्य अहम् आत्मा सन् हृदि बुद्धौ संनिविष्टः । अतः मत्तः आत्मनः सर्वप्राणिनां स्मृतिः ज्ञानं तदपोहनं च अपगमनं च ; येषां यथा पुण्यकर्मणां पुण्यकर्मानुरोधेन ज्ञानस्मृती भवतः, तथा पापकर्मणां पापकर्मानुरूपेण स्मृतिज्ञानयोः अपोहनं च अपायनम् अपगमनं च । वेदैश्च सर्वैः अहमेव परमात्मा वेद्यः वेदितव्यः । वेदान्तकृत् वेदान्तार्थसम्प्रदायकृत् इत्यर्थः, वेदवित् वेदार्थवित् एव च अहम् ॥ १५ ॥
In plain words
And there's more —
And I, as the Self, dwell within every kind of living being, seated right there in the heart, in the understanding itself. That is why memory and knowledge, and their loss, their vanishing, all come from Me, from the Self within every creature. For those whose deeds are good, knowledge and memory arise in proportion to that goodness; and for those whose deeds are bad, that same memory and knowledge fade away, in proportion to that badness. And it is I, the Supreme Self, and no other, whom all the Vedas together exist to make known. I am the very author of Vedānta, the one who establishes its handed-down meaning, and I am the knower of the Veda, the knower of what the Veda truly means.
Close to the Sanskrit
Moreover —
And of all the multitude of living beings, I, being the Self, am seated in the heart, in the intellect. Therefore, from Me, from the Self, of all living beings, come memory, knowledge, and the removal of that, and the departure of it; for whomsoever, as with good deeds, in accordance with good deeds, knowledge and memory arise, so, for those of bad deeds, in accordance with bad deeds, there is the removal of memory and knowledge, and the departure of them. And by all the Vedas, I alone, the Supreme Self, am to be known, to be understood. I am the maker of Vedānta, the establisher of the tradition of the meaning of Vedānta — that is the meaning; and I am the knower of the Veda, the knower of the meaning of the Veda, indeed. || 15 ||