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Axiomatic, analytic, transformational, and algebraic approaches to geometry will be used. The relationship between Euclidean geometry, the geometry of advanced numbers, and trigonometry shall be emphasised. Topics embrace internal product spaces, norms, self adjoint and regular operators, orthogonal and unitary operators, orthogonal projections and the spectral theorem, bilinear and quadratic types, generalized eigenvectors, and Jordan canonical kind.

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