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  • https://math.libretexts.org/Bookshelves/Differential_Equations/Applied_Linear_Algebra_and_Differential_Equations_(Chasnov)/02%3A_II._Linear_Algebra/01%3A_Matrices/1.04%3A_Rotation_Matrices_and_Orthogonal_Matrices
    Trigonometry and the addition formula for cosine and sine results in \[\begin{aligned} x'&=r\cos(\theta+\psi) \\ &=r(\cos\theta\cos\psi -\sin\theta\sin\psi )\\&=x\cos\theta-y\sin\theta \\ y'&=r\sin(\t...Trigonometry and the addition formula for cosine and sine results in x=rcos(θ+ψ)=r(cosθcosψsinθsinψ)=xcosθysinθy=rsin(θ+ψ)=r(sinθcosψ+cosθsinψ)=xsinθ+ycosθ. Writing the equations for x and y in matrix form, we have \[\left(xy\right)=\left(\begin{array}{rr}\cos\theta&-\sin\theta \\ \sin\theta&\cos\theta\…
  • https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/07%3A_Appendix/7.01%3A_A_-_Complex_Numbers
    This page reviews the arithmetic of complex numbers, introducing the imaginary unit i and defining complex numbers as a+bi. It covers operations such as addition, multiplication, and complex...This page reviews the arithmetic of complex numbers, introducing the imaginary unit i and defining complex numbers as a+bi. It covers operations such as addition, multiplication, and complex conjugation. The Fundamental Theorem of Algebra is discussed, stating that every polynomial of degree n has n complex roots, including complex conjugates. Examples are provided to demonstrate how to find these complex roots.

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