In plain words
Because I transcend the perishable and am higher even than the imperishable, I am celebrated in the world and in the Veda as Purushottama.
Word for word
Since I have gone beyond the perishable and [am] higher even than the imperishable, therefore I am renowned in the world and in the Veda [as] Puruṣottama.
यस्मात् क्षरमतीतोऽहम् अक्षरादपि चोत्तमःअतोऽस्मि लोके वेदे च प्रथितः पुरुषोत्तमः
Other commentaries
The commentators
▸Bhagavadgītābhāṣyam
यथाव्याख्यातस्य ईश्वरस्य ‘पुरुषोत्तमः’ इत्येतत् नाम प्रसिद्धम् । तस्य नामनिर्वचनप्रसिद्ध्या अर्थवत्त्वं नाम्नो दर्शयन् ‘निरतिशयः अहम् ईश्वरः’ इति आत्मानं दर्शयति भगवान् —
यस्मात् क्षरम् अतीतः अहं संसारमायावृक्षम् अश्वत्थाख्यम् अतिक्रान्तः अहम् अक्षरादपि संसारमायारूपवृक्षबीजभूतादपि च उत्तमः उत्कृष्टतमः ऊर्ध्वतमो वा, अतः ताभ्यां क्षराक्षराभ्याम् उत्तमत्वात् अस्मि लोके वेदे च प्रथितः प्रख्यातः । पुरुषोत्तमः इत्येवं मां भक्तजनाः विदुः । कवयः काव्यादिषु च इदं नाम निबध्नन्ति । पुरुषोत्तम इत्यनेनाभिधानेनाभिगृणन्ति ॥ १८ ॥
In plain words
This Lord, described just as we have explained him, is well known by the name Puruṣottama, the Supreme Person. Now, drawing out the meaning hidden in that very name through its well-known derivation, and thereby declaring, 'I am the Lord beyond all others,' the Lord now reveals himself —
Because I have gone beyond the perishable, beyond that tree of saṃsāra and māyā called the Aśvattha, and because I have gone beyond even the imperishable, which is itself the very seed from which that tree of saṃsāra and māyā grows, I am the highest, the very best, the one above all. And so, being superior to both the perishable and the imperishable, I am renowned, celebrated, both in this world and in the Veda. This is how devotees know Me: as Puruṣottama, the Supreme Person. Poets weave this very name into their poetry, and with this one word, Puruṣottama, they proclaim who I am.
Close to the Sanskrit
Of the Lord as thus explained, 'Puruṣottama' — this name is well-known. Showing, by the well-known etymological explanation of that name, the meaningfulness of the name — 'I am the unsurpassed Lord' — thus the Lord shows himself —
Because I have transcended the perishable, gone beyond the tree of saṃsāra-māyā called Aśvattha; I transcend even the imperishable, which is the very seed of that same tree in the form of saṃsāra-māyā; I am the highest, the most excellent, or the topmost; therefore, on account of my superiority to those two, the perishable and the imperishable, I am renowned, celebrated, in the world and in the Veda. 'Puruṣottama,' thus do devotees know Me. Poets, in poetry etc., fix this name. By this very appellation, 'Puruṣottama,' they proclaim Me. || 18 ||