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

单词

Diagonal Matrix

释义

Diagonal Matrix

A diagonal matrix is a Matrix of the form

(1)

where

is the Kronecker Delta,

are constants, and there is no summation over indices. The generaldiagonal matrix is therefore Square and of the form

(2)

Given a Matrix equation of the form

(3)

multiply through to obtain

(4)

Since in general,

for

, this can be true only if off-diagonal components vanish.Therefore, A must be diagonal.

Given a diagonal matrix ,

(5)

See also Matrix, Triangular Matrix, Tridiagonal Matrix

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 181-184 and 217-229, 1985.

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