MathNotes - algebra

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For a linear map between finite-dimensional vector spaces, dim(V) = rank(T) + nullity(T).

\dim(V) = \operatorname{rank}(T) + \operatorname{nullity}(T)

Every real symmetric matrix is orthogonally diagonalisable with real eigenvalues.

A=A^\top\implies A=QDQ^\top,\quad Q\text{ orthogonal}

Linear Algebra