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Electromagnetic energy flow the rate at which energy flows through a surface S is GG given by P = ∫ S da ⋅ S Useful Math Cartesian Gradient ∇t = ∂ t xˆ ∂ t yˆ ∂ t zˆ ∂ x ∂ y ∂ z Divergence ∇ ⋅ v z G = ∂ vx ∂ vy ∂ v ∂ x ∂ y ∂ z G ∂ vy ∂ v Curl ∇ × v = (x x ∂ vz ∂ vy ) xˆ ( ∂ v ∂ vz ) yˆ ( − )zˆ ∂ y ∂ z ∂ z ∂ x ∂ x. C ^ X g E v _ N V. Vn kvnk Then w1,w2,,wn is an orthonormal basis for V Theorem Any finitedimensional vector space with an inner product has an orthonormal basis Remark An infinitedimensional vector space with an inner product may or may not have an orthonormal basis Title.

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