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Linear Algebra Lecture 26 | Every Finite Dimensional Vector Space Has a Basis. NET/JRF
Автор: gamowmaths
Загружено: 2025-08-19
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Описание:
In this lecture, we prove one of the most fundamental results in linear algebra:
✅ Every finite-dimensional vector space has a basis.
We begin by revisiting the definition of basis, independent sets, and span.
We also explain the special case of the zero space and how the empty set acts as its basis.
Then, step by step, we prove the theorem that every spanning set contains a basis and conclude that every finite-dimensional vector space has a basis.
This lecture is part of my Linear Algebra playlist for undergraduate and NET/JRF mathematics preparation.
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