Bhagavad Gita · Purushottama YogaChapter 15, Shloka 1 (15.1)

Shankaracharya. ūrdhvamūlaṃ kālataḥ sūkṣmatvāt kāraṇatvāt nityatvāt mahattvāc ca ūrdhvam ucyate brahma avyaktaṃ māyāśaktimat, tat mūlam asya — the root is "above": subtle in time, the cause, eternal, great — the unmanifest Brahman endowed with the power of maya; his authority is the Katha; "ashvattha" — na śvo'pi sthātā (that which will not last even till tomorrow), the traditional derivation.

Acharya Ramanuja. yaṃ saṃsārākhyam aśvattham ūrdhvamūlam adhaḥśākham avyayaṃ prāhuḥ śrutayaḥ — that which the shrutis call the ashvattha of worldly existence; saptalokopari niviṣṭacaturmukhādi… — the root = four-faced Brahma, seated above the seven worlds.

Shridhara Swami. The purpose of the chapter in a single verse: vairāgyeṇa vinā jñānaṃ na ca bhaktir ataḥ sphuṭam, vairāgyopaskṛtaṃ jñānam īśaḥ pañcadaśe 'diśat — without dispassion there is neither knowledge nor devotion; therefore in the fifteenth chapter the Lord gave knowledge joined with dispassion. For him the "root above" = uttamaḥ kṣarākṣarābhyām utkṛṣṭaḥ puruṣottamo mūlaṃ — Purushottama himself is the root.

Madhusudana Saraswati. He regards this chapter as the vṛttisthānīya — the commentary — of 14.27 (brahmaṇo hi pratiṣṭhāham): that verse was the sutra, this chapter its commentary.

Madhvacharya. The derivation of "ashvattha": śvo 'py ekaprakāreṇa na tiṣṭhatīty aśvatthaḥ — that which does not remain in one form even till tomorrow; and yet na pravāhavyayaḥ — its flow does not perish. And why are the Vedas the leaves: na hi kadācid apy ajāte parṇe phalotpattiḥ — without leaves, no fruit appears.