| 41. | Given, with being a unit vector, the correct skew-symmetric matrix form of "'? "'is
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| 42. | Conversely, given a quadratic form in " n " variables, its coefficients can be arranged into an symmetric matrix.
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| 43. | Here the numerator is a symmetric matrix while the denominator is a number, the squared magnitude of "'v " '.
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| 44. | Going the other direction, the matrix exponential of any skew-symmetric matrix is an orthogonal matrix ( in fact, special orthogonal ).
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| 45. | The integers m _ { i, j } can be organized into a symmetric matrix, known as the Coxeter matrix of the group.
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| 46. | Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
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| 47. | The components of a metric tensor in a coordinate basis take on the form of a symmetric matrix whose entries transform smoothly from point to point.
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| 48. | Augustin-Louis Cauchy proved the spectral theorem for self-adjoint matrices, i . e ., that every real, symmetric matrix is diagonalizable.
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| 49. | Therefore, in linear algebra over the complex numbers, it is often assumed that a symmetric matrix refers to one which has real-valued entries.
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| 50. | This is an example of a symmetric bilinear form which is not associated to any symmetric matrix ( since the vector space is infinite-dimensional ).
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