Validity of “no of genereralized eigen vectors = algebraic multiplicity” in the domain of real numbers

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Suppose a matrix has no'of real eigen values less than its order $n$. Then are the following identities valid in the domain of real numbers?

no'of genereralized eigen vectors $=$ algebraic multiplicity

Algebraic multiplicity $geq$ geometric multiplicity

edited Dec 2 at 4:28

asked Dec 2 at 4:03

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Suppose a matrix has no'of real eigen values less than its order $n$. Then are the following identities valid in the domain of real numbers?

no'of genereralized eigen vectors $=$ algebraic multiplicity

Algebraic multiplicity $geq$ geometric multiplicity

edited Dec 2 at 4:28

asked Dec 2 at 4:03

Akhil

New contributor

add a comment |

up vote
1
down vote

favorite

Suppose a matrix has no'of real eigen values less than its order $n$. Then are the following identities valid in the domain of real numbers?

no'of genereralized eigen vectors $=$ algebraic multiplicity

Algebraic multiplicity $geq$ geometric multiplicity

edited Dec 2 at 4:28

asked Dec 2 at 4:03

Akhil

New contributor

Suppose a matrix has no'of real eigen values less than its order $n$. Then are the following identities valid in the domain of real numbers?

no'of genereralized eigen vectors $=$ algebraic multiplicity

Algebraic multiplicity $geq$ geometric multiplicity

linear-algebra

edited Dec 2 at 4:28

asked Dec 2 at 4:03

Akhil

New contributor

edited Dec 2 at 4:28

asked Dec 2 at 4:03

Akhil

New contributor

edited Dec 2 at 4:28

asked Dec 2 at 4:03

Akhil

New contributor

asked Dec 2 at 4:03

Akhil

asked Dec 2 at 4:03

Akhil

New contributor

Akhil is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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