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Diagonalizable matrix
Geometrically, a diagonalizable matrix is an inhomogeneous dilation (or anisotropic scaling) — it scales the space, as does a homogeneous dilation, but by a ...


可對角化矩陣 (Diagonalizable matrix)


可對角化矩陣是線性代數和矩陣論中重要的一類矩陣。如果一個方塊矩陣 A 相似於對角矩陣,也就是說,如果存在一個可逆矩陣 P 使得 P ⁻¹AP 是對角矩陣,則它就被稱為可對角化的。如果 V 是有限維度的向量空間,則線性映射 T: V → V 被稱為可對角化的,如果存在 V 的一個基,T 關於它可被表示為對角矩陣。 维基百科
作者:EW Weisstein2000 — may be tested to determine if it is diagonalizable in the Wolfram Language using DiagonalizableMatrixQ[m]. ... . Matrix diagonalization (and most other forms of ...
(-1,0,1)-matrix: A091470
(0,1)-matrix: A091472
Matrix type: OEIS
(-1,1)-matrix: A091471
2013年4月19日 — A square matrix which is not diagonalizable is called defective. Diagonalizable matrices and maps are of interest because diagonal matrices are ...
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A diagonalizable matrix is any square matrix or linear map where it is possible to sum the eigenspaces to create a corresponding diagonal matrix.
An n × n matrix A is diagonalizable if and only if A has n linearly independent eigenvectors. In this case, A = CDC − ...
A square matrix is said to be diagonalizable if it is similar to a diagonal matrix. That is, A A A is diagonalizable if there is an invertible matrix P P P ...
2020年4月6日 — One important application of diagonalizable matrices is computing powers of ... for a n × n diagonal matrix D and n × n invertible matrix P.
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Diagonalizable matrix — Not all matrices are diagonalizable. The diagonalizable matrices are those that have no defective eigenvalues (i.e., eigenvalues ...

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