## Linear Operators, Part 1 |

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Page 45

With this notation the number expressed by the sum n n din ..... ini ,, 1 , ... , Ainon

21 = 1 is called the determinant of the

it can be shown that the determinants of the

With this notation the number expressed by the sum n n din ..... ini ,, 1 , ... , Ainon

21 = 1 is called the determinant of the

**matrix**( aij ) . If T is a linear operator , thenit can be shown that the determinants of the

**matrices**of T in terms of any two ...Page 561

The

Pn ( P ) . ... for all

etA form a set of m linearly independent solutions of the equation dy / dt Ay .

The

**matrix**P. ( Pii ) defines a linear transformation in E52 whose n - th power isPn ( P ) . ... for all

**matrices**A in Em . Since e - 14ctA = 1 , the columns of the**matrix**etA form a set of m linearly independent solutions of the equation dy / dt Ay .

Page 564

19 Find the most general solution of the differential equation y ' = Ty where T is

the

systems of n linear homogeneous differential equations , dy ( t ) / dt = A ( t ) y .

Here A ...

19 Find the most general solution of the differential equation y ' = Ty where T is

the

**matrix**of Exercise 5 . The next ten exercises refer to the stability theory ofsystems of n linear homogeneous differential equations , dy ( t ) / dt = A ( t ) y .

Here A ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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