1141: Hermitian Conjugate of Complex Matrix

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definition of Hermitian conjugate of complex matrix

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Topics

About: matrices space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Note

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Starting Context

• The reader knows a definition of complex conjugate of complex matrix.
• The reader knows a definition of transpose of matrix.

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Target Context

• The reader will have a definition of Hermitian conjugate of complex matrix.

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Orientation

There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$M$: $\in \{\text{ the }m\times n\text{ complex matrices }\}$
$\ast M^{\ast }$: $={\bar{M}}^t$, $\in \{\text{ the }n\times m\text{ complex matrices }\}$
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Conditions:
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2: Note

Obviously, ${\bar{M}}^t=\overline{M^t}$.

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References

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