tataḥ śvetavrajāḥ vīraḥ śvetāśvāḥ mātuleḥ avaśāt

tataḥ (then) śvetavrajāḥ (having white or shining encampment/ tents) vīraḥ (the hero) śvetāśvāḥ (having white horses) mātuleḥ (from maternal uncle's place/ or a particular region) avaśāt (obtained/ got)

Advaita Vedānta (Ādi Śaṅkarācārya): This verse, tataḥ śvetavrajā vīraḥ śvetāśvā mātule 'vaśāt, points to the ultimate reality of Brahman through the metaphor of the 'white-complexioned people' and 'white horses.' According to Shankara, such descriptions are meant to guide the mind towards the immutable and pure essence of the Self (Ātman), which is beyond all dualities and attributes. The reference to 'mātule' (related to the maternal lineage or the Vindhya region) can be seen as an allegory for the conditioned self (jīva) coming under the influence of Māyā, yet yearning for the pure, unconditioned state symbolized by the white horses and the heroic lineage. This yearning is the spark that initiates the quest for Self-realization, leading to the understanding of the brahman-ātman identity, where the individual self (jīva) recognizes its non-dual nature with the universal Self (Brahman). Shankara's emphasis on the importance of understanding and removing ignorance (avidyā) to achieve this realization underscores the significance of such metaphors in guiding the seeker towards the ultimate truth.

Vaiṣṇava tradition (Rāmānujācārya / Madhvācārya): The Vaiṣṇava interpretation of this verse would likely focus on the devotional aspect and the relationship between the jīva (the individual soul) and Īśvara (the Supreme Lord). Rāmānujācārya might see the 'white-complexioned people' and 'white horses' as symbols of the pious and the righteous, whose actions and intentions are as pure as white, indicating their devotion to and grace of the Supreme Being. The 'mātule' could be understood as the divine providence or the Lord's will, under which all activities, including those of the pious and the heroic, are guided. This reading underscores the Vaiṣṇava concept of 'prapatti' or surrender, where the jīva, recognizing its inherent dependence on Īśvara, surrenders to the divine will, much like the horses and the heroic lineage are under the control of a higher power. Madhvācārya, with his emphasis on the distinction between the Lord and the souls, might further detail the separate yet interconnected roles of Īśvara and the jīvas in this context, highlighting the dependency of all beings on the divine for their very existence and actions.

Neo-Vedānta (Swami Vivekānanda / S. Rādhākrishnan): Swami Vivekānanda would likely interpret this verse in the light of the universal principles applicable to human life and spiritual growth. The 'white-complexioned people' and 'white horses' could symbolize purity, simplicity, and the innate goodness in every being. The idea of these heroic lineages emerging 'under the control of Mātṛ' could be seen as the influence of the maternal principle or nature that shapes human character and destiny. This principle is reminiscent of Vivekānanda's emphasis on the importance of recognizing and harmonizing with nature, as well as the maternal aspect of the divine that nurtures and guides humanity. In contemporary life, this verse could be a call to return to simplicity, purity, and harmony with nature, recognizing the interconnectedness of all beings and the universe. It also points to the potential within each individual to embody heroic qualities, guided by a higher power or principle, leading to a more meaningful and purposeful existence. This interpretation aligns with Vivekānanda's philosophy of practical Vedānta, which seeks to apply the timeless principles of Vedānta to everyday life for the betterment of society and the individual.

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