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Two vectors are orthogonal if and only if the Pythagorean Theorem holds.
Unitary matrices
Unitary matrices are invertible.
Unitary matrices have orthogonal (orthonormal) rows/columns.
Unitary matrices preserve inner products.
Unitary matrices preserve orthogonal (orthonormal) bases.
Using matrices to solve linear systems
Vector space isomorphism is an equivalence relation.
Vector spaces
Vector spaces with the same dimension are isomprphic.
Vector sum/addition interpreted geometrically in R^n (or C^n)
Vector sum/addition is commutative and associative
Visualise a linear transformation on R^2 by looking at the image of a region

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