linearly independent
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1: 29.17 Other Solutions
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►If (29.2.1) admits a Lamé polynomial solution , then a second linearly independent solution is given by
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2: 28.5 Second Solutions ,
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►If a nontrivial solution of Mathieu’s equation with has period or , then any linearly independent solution cannot have either period.
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►As a consequence of the factor on the right-hand sides of (28.5.1), (28.5.2), all solutions of Mathieu’s equation that are linearly independent of the periodic solutions are unbounded as on .
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3: 14.2 Differential Equations
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►When , and , and are linearly independent, and when they are recessive at and , respectively.
…When , or , and are linearly dependent, and in these cases either may be paired with almost any linearly independent solution to form a numerically satisfactory pair.
►When and , and are linearly independent, and recessive at and , respectively.
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4: 1.13 Differential Equations
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►The following three statements are equivalent: and comprise a fundamental pair in ; does not vanish in ; and are linearly independent, that is, the only constants and such that
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5: 3.2 Linear Algebra
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►To an eigenvalue of multiplicity , there correspond
linearly independent eigenvectors provided that is nondefective, that is, has a complete set of
linearly independent eigenvectors.
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