Hi I need some help remembering the definition and conditions of a basis:
In which way can the following implications go?
1) => 2), 2) => 1) or both?
1) A basis for a subspace or any space has to satisfy the following 2 conditions:
a) be linearly independent, b) span the subspace;
2) The "Basis theorem 15" in David C. Lay's 3rd edition of Linear Algebra and its applications says:
Let H be a p-dimensional subspace of R^n. Any linearly independent set of exactly p elements in H is automatically a basis for H. Also, any set of p elements of H that spans H is automatically a basis for H.

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