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In linear algebra, skew-Hamiltonian matrices are special matrices which correspond to skew-symmetric bilinear forms on a symplectic vector space. Let V be a vector space, equipped with a symplectic form . Such a space must be even-dimensional. A linear map is called a skew-Hamiltonian operator with respect to if the form is skew-symmetric. Choose a basis in V, such that is written as . Then a linear operator is skew-Hamiltonian with respect to if and only if its matrix A satisfies , where J is the skew-symmetric matrix

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  • Matrice anti-hamiltoniana (it)
  • Skew-Hamiltonian matrix (en)
  • 斜漢彌爾頓矩陣 (zh)
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  • In algebra lineare, le matrici anti-hamiltoniane sono speciali matrici che corrispondono a forme bilineari antisimmetriche su uno spazio vettoriale simplettico. (it)
  • 在線性代數當中，斜漢彌爾頓矩陣是一類與在辛向量空间上的双线性映射相對應的矩陣。 設V為一個向量空間，在其上有著辛形式。則如此的空間其維度必然是偶數維的。在此空間中，當「是斜對稱的」這條件滿足時，一個線性映射被稱作對的斜漢彌爾頓算子（skew-Hamiltonian operator）。 在V中選擇適當的基使得可寫成這樣的形式，那麼一個線性算子被稱為是一個對的斜漢彌爾頓算子，當且僅當當且僅當在這個基中與此算子對應的矩陣A滿足這條件，而J則是一個有如下形式的反對稱矩陣： 其中In是階矩陣的單位矩陣。滿足這條件的矩陣就被稱為斜漢彌爾頓矩陣（skew-Hamiltonian matrix）。 一個漢彌爾頓矩陣的平方是一個斜漢彌爾頓矩陣。這反過來也成立，也就是說，任何的斜漢彌爾頓矩陣都是一個漢彌爾頓矩陣平方。 (zh)
  • In linear algebra, skew-Hamiltonian matrices are special matrices which correspond to skew-symmetric bilinear forms on a symplectic vector space. Let V be a vector space, equipped with a symplectic form . Such a space must be even-dimensional. A linear map is called a skew-Hamiltonian operator with respect to if the form is skew-symmetric. Choose a basis in V, such that is written as . Then a linear operator is skew-Hamiltonian with respect to if and only if its matrix A satisfies , where J is the skew-symmetric matrix (en)
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  • In linear algebra, skew-Hamiltonian matrices are special matrices which correspond to skew-symmetric bilinear forms on a symplectic vector space. Let V be a vector space, equipped with a symplectic form . Such a space must be even-dimensional. A linear map is called a skew-Hamiltonian operator with respect to if the form is skew-symmetric. Choose a basis in V, such that is written as . Then a linear operator is skew-Hamiltonian with respect to if and only if its matrix A satisfies , where J is the skew-symmetric matrix and In is the identity matrix. Such matrices are called skew-Hamiltonian. The square of a Hamiltonian matrix is skew-Hamiltonian. The converse is also true: every skew-Hamiltonian matrix can be obtained as the square of a Hamiltonian matrix. (en)
  • In algebra lineare, le matrici anti-hamiltoniane sono speciali matrici che corrispondono a forme bilineari antisimmetriche su uno spazio vettoriale simplettico. (it)
  • 在線性代數當中，斜漢彌爾頓矩陣是一類與在辛向量空间上的双线性映射相對應的矩陣。 設V為一個向量空間，在其上有著辛形式。則如此的空間其維度必然是偶數維的。在此空間中，當「是斜對稱的」這條件滿足時，一個線性映射被稱作對的斜漢彌爾頓算子（skew-Hamiltonian operator）。 在V中選擇適當的基使得可寫成這樣的形式，那麼一個線性算子被稱為是一個對的斜漢彌爾頓算子，當且僅當當且僅當在這個基中與此算子對應的矩陣A滿足這條件，而J則是一個有如下形式的反對稱矩陣： 其中In是階矩陣的單位矩陣。滿足這條件的矩陣就被稱為斜漢彌爾頓矩陣（skew-Hamiltonian matrix）。 一個漢彌爾頓矩陣的平方是一個斜漢彌爾頓矩陣。這反過來也成立，也就是說，任何的斜漢彌爾頓矩陣都是一個漢彌爾頓矩陣平方。 (zh)
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