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First, note that the word Brahmi is not found anywhere in the Sanskrit verse. It was inserted by the translator. But, anyway, it's talking about BrAhmi, the foremost among the Ashta Matrika Shaktis. And, "the other powers" are the remaining 7 Shaktis of the group (names of whom are given later in this answer). We find their mentions throughout ...


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Acharya Abhinavagupta, in his Gitartha Samgraha explicitly regards the Vedas as the highest authority on Dharma. This is what he comments on the following verses from the Bhagavad Gita which appears to be a criticism of the Vedas: 2.43 The undisceming, delighting in the study of the Veda,O Partha, speak flowery words declaring that there is nothing else. ...


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The main exegetical works of Kashmir Shavism (Trika Shavism) are those of Abhinavagupta such as the Tantraloka amongst others, and this drew heavily on the Kali-based Krama subcategory of the Kulamarga. Hence it isn't a sub-school, more of an influence. The influence is easy enough to discern once its understood that the important Krama texts, Kalikrama, ...


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I read the same book and did some research after coming across this claim - So here's a link I'm providing which (at some extent) was helpful for me on this topic ... https://www.ikashmir.net/saints/shankracharyavisittokashmir.html Also ..he wasn't actually "defeated" , rather ..he accepted the pre-dominance of "shakti-cult" (the greatness of Devi) as was ...


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