The discussion revolves around understanding the concept of "vector bases" in the context of quantum mechanics, specifically referencing Ramamurti Shankar's textbook. The original poster seeks clarification on what a vector basis means and its application in solving equations in an eigenvector basis.
Some participants have offered clarifications regarding the definition of a basis and its role in spanning vector spaces. There is an ongoing exploration of the term "eigenvector basis," with participants seeking further understanding of its implications in quantum mechanics.
The original poster's inquiry suggests a potential misunderstanding of terminology, as they refer to "vector base" instead of "vector basis." This may indicate a need for foundational clarification in the subject matter.
Yes, a basis can be used to generate all possible vectors in the vector space or subspace spanned by the vectors in the basis. In the simple example in my previous post, every vector in R2 is a linear combination (the sum of scalar multiples) of the vectors in the basis. E.g., (3, 5) = 3(1, 0) + 5(0, 1).player1_1_1 said:thanks for help, and this basis is vectors which can be used to create any possible vector in this space? what is a "eigenvector basis" or something? i saw it somewhere