| 31. | :Note that the important part here is the " p " linearly independent eigenvectors.
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| 32. | Fourth, a matrix is invertible if the columns are linearly independent, hence P is invertible.
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| 33. | Since this is a second-order differential equation, we must have two linearly independent solutions.
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| 34. | The strain rate tensor is symmetric by definition, so it has only six linearly independent elements.
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| 35. | The atoms in A as well as the atoms in B are assumed to be linearly independent.
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| 36. | If multiple linearly independent eigenfunctions have the same eigenvalue, the eigenvalue is said to be geometric multiplicity.
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| 37. | One seeks conditions on the existence of a collection of solutions such that the gradients are linearly independent.
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| 38. | Of which the first three are easily seen to be linearly independent, and therefore span all of.
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| 39. | The most general solution will be a linear combination of linearly independent solutions to the above homogeneous equation.
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| 40. | I now have to find a linearly independent branch, which I am unsure of how to do.
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