User Zizo - Mathematics Stack Exchange

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	380 reputation	bio	website		visits	member for	1 year, 5 months
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1

6

votes

3

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147

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Simplicity of eigenvalue

feb 20 at 21:19 user1551 16.5k

3

6

votes

3

answers

771

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Infinite sum of geometric series of a matrix

linear-algebra analysis matrices

dec 1 '11 at 15:59 Zizo 380

4

5

votes

2

answers

813

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How to show if $ \lambda$ is an eigenvalue of $AB^{-1}$, then $ \lambda$ is an eigenvalue of $ B^{-1}A$?

linear-algebra matrices functional-analysis

dec 29 '11 at 20:00 Zizo 380

2

3

votes

2

answers

2

kviews

A matrix and its transpose have the same set of eigenvalues

linear-algebra matrices

sep 9 at 17:06 Peter Tamaroff 25.3k

3

votes

3

answers

77

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Let $|\lambda|<1$. Show that $ \lim_{k \rightarrow \infty} \frac{k^j}{j!}| \lambda|^{ k -j} = 0 $ where $ j = 1,2, \dots, m.$

calculus real-analysis sequences-and-series

mar 7 '12 at 18:12 Thomas 10.8k

3

votes

1

answer

81

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Let $ \rho(P)$ be the spectral radius of $P$. Show $ \rho( \dfrac{P}{ \rho(P) + \epsilon } ) < 1 \text{ for all } \epsilon >0. $

linear-algebra matrices functional-analysis

feb 9 '12 at 14:33 Ilya 14.2k

2

votes

2

answers

110

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Some facts about matrix norm

linear-algebra matrices

dec 23 at 17:27 user1551 16.5k

2

votes

1

answer

97

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Inequality from a matrix norm

linear-algebra real-analysis matrices

dec 18 at 4:21 user1551 16.5k

2

votes

2

answers

217

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Minimum and Maximum eigenvalue inequality from a positive definite matrix.

linear-algebra matrices

nov 27 at 19:50 dineshdileep 2,141

2

votes

0

answers

168

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Spectral radius and positive definite of matrices

linear-algebra matrices spectral-theory

oct 26 at 22:51 Martin Argerami 16.8k

2

votes

1

answer

303

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A primitive and irreducible matrix is positive for some power $k.$ Prove it's positive for any power $k+i,$ where $i=1,\dots.$

linear-algebra matrices functional-analysis

aug 14 at 20:53 Community♦ 1

2

votes

2

answers

231

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The compactness of the unit sphere in finite dimensional normed vector space

linear-algebra matrices functional-analysis semigroups

mar 7 '12 at 9:07 Patrick Da Silva 13.3k

2

votes

0

answers

167

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Primitive matrices has positive powers.

linear-algebra matrices functional-analysis

jan 24 '12 at 14:41 Zizo 380

1

vote

3

answers

40

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Graph of a matrix and a positive power for the the matrix

matrices graph-theory

mar 10 at 7:41 Alexander Gruber 15.1k

1

vote

2

answers

70

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Point of maximum modulus of a circular disk

complex-analysis

nov 5 at 20:56 copper.hat 28.4k

1

vote

1

answer

89

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Strongly connected graph associated with a matrix

matrices graph-theory spectral-graph-theory

nov 2 at 10:38 Jesko Hüttenhain 3,293

1

vote

2

answers

215

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If the spectral radius of a matrix is less than 1, then the matrix has a norm which is less than 1.

linear-algebra matrices

oct 10 at 9:31 Pantelis Damianou 2,679

1

vote

1

answer

79

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Positive definite of infinite sum of matrices

linear-algebra matrices

oct 6 at 7:31 Zizo 380

1

vote

2

answers

88

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Let $z \in \mathbb{C}^m.$ Then $\| \sum_{j} z_j \|_2 = \sum_j \| z_j \|_2 \Longleftrightarrow z_j = \alpha_j z_1$ for some $ \alpha_j>0.$

linear-algebra matrices vector-spaces

apr 1 '12 at 16:21 Martin Argerami 16.8k

1

vote

2

answers

339

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Does the left and right eigenvector of a matrix corresponding to different eigenvalues ALWAYS have a zero dot product?

linear-algebra analysis matrices functional-analysis

dec 10 '11 at 21:53 Arturo Magidin 158k

0

votes

1

answer

46

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The $h-$th power of every element in a finite group of order $h$ is the identity element of the group

group-theory finite-groups

nov 29 at 7:31 Jernej 1,134

0

votes

2

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130

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If a matrix power has a limit which is positive, then there exists some power of the matrix such that the matrix is positive for this power.

linear-algebra matrices

nov 13 at 13:28 YoungFrog 46

0

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1

answer

154

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Convergence of infinite series of converge matrices.

linear-algebra matrices

oct 6 at 8:33 Did 102k

0

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3

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74

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$ \lim_{ k \rightarrow \infty } { \frac{ \lambda^k }{k}} = \infty$ when $1 < |\lambda| \in \mathbb{C} $.

real-analysis sequences-and-series

jul 9 at 17:15 Michael Hardy 47.7k

0

votes

1

answer

132

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Let $ \omega \in \sigma(P^k).$ If $\omega = \lambda^ k$ then $ \lambda \in \sigma(P).$

linear-algebra matrices functional-analysis

feb 22 '12 at 0:34 Zizo 380

0

votes

1

answer

82

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Induction problems

calculus real-analysis

feb 21 '12 at 10:36 Alex Becker 27.7k

0

votes

1

answer

145

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what does $o(|x|^2)$ stand for?

calculus real-analysis

jan 12 '12 at 12:34 David Mitra 40.9k

0

votes

1

answer

153

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Let $\mathbb{R}^m_+ = \lbrace x \in \mathbb{R}^m : x \geqslant 0 \rbrace.$ What is the boundary set of the set $ \mathbb{R}^m_+$?

general-topology differential-topology

jan 12 '12 at 10:42 Clive Newstead 15.2k

0

votes

1

answer

83

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Primitive matrices

linear-algebra matrices

dec 2 '11 at 15:38 Stuart 809

Zizo

29 Questions