Proofs
Browse a catalog of interesting and common proofs, from core analysis and linear algebra arguments to standard proof techniques worth knowing well.
Showing 3 proofs in Linear Algebra.
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Proof that the kernel of a linear map is a subspace
This is a standard linear algebra proof because it packages the subspace test into one reusable pattern: show zero is inside, then check closure under addition and scalar multiplication.
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Proof that eigenvectors for distinct eigenvalues are linearly independent
Distinct eigenvalues do more than label eigenspaces. They force eigenvectors to be independent, which is exactly why diagonalization becomes possible so often in practice.
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Proof that the composition of linear maps is linear
Composing two linear maps does not break linearity. The proof is a careful unpacking of definitions: first pass through the inner map, then use linearity again in the outer map.
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