“Antisymmetric Matrix”的概念、定义、习题解题方法及翻译-数学辞典

单词

Antisymmetric Matrix

释义

Antisymmetric Matrix

An antisymmetric matrix is a Matrix which satisfies the identity

(1)

where

is the Matrix Transpose. In component notation, this becomes

(2)

Letting

, the requirement becomes

(3)

so an antisymmetric matrix must have zeros on its diagonal. The general

antisymmetric matrix is of the form

(4)

Applying to both sides of the antisymmetrycondition gives

(5)

Any Square Matrix can be expressed as the sum of symmetric and antisymmetric parts. Write

(6)

But

(7)

(8)

(9)

which is symmetric, and

(10)

which is antisymmetric.

See also Skew Symmetric Matrix, Symmetric Matrix

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