| Information | |
|---|---|
| has gloss | eng: In linear algebra, a tridiagonal matrix is a matrix that is "almost" a diagonal matrix. To be exact: a tridiagonal matrix has nonzero elements only in the main diagonal, the first diagonal below this, and the first diagonal above the main diagonal. |
| lexicalization | eng: Tri-diagonal matrix |
| lexicalization | eng: Tridiagonal Matrix |
| instance of | (noun) (mathematics) a rectangular array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules matrix |
| Meaning | |
|---|---|
| German | |
| has gloss | deu: In der linearen Algebra ist eine Tridiagonalmatrix (auch: Dreibandmatrix) eine quadratische Matrix T\in\mathbbC}^n\times n}, die nur in der Diagonalen und in den beiden ersten Nebendiagonalen Einträge ungleich Null enthält, es gilt also t_ij}=0 für alle |i-j| > 1. Eine Tridiagonalmatrix heißt unreduziert oder irreduzibel, wenn die Elemente in den Nebendiagonalen alle ungleich Null sind. (daher :t_ij} \not= 0 für alle |i-j|=1). |
| lexicalization | deu: Tridiagonalmatrix |
| Esperanto | |
| has gloss | epo: Tridiagonala matrico estas matrico kiu havas formon: : \mathbfA}= \beginbmatrix} b_1 & a_2 & 0 & 0 & 0 \\ a_2 & b_2 & a_3 & 0 & 0 \\ 0 & a_3 & \ddots & \ddots & 0 \\ \vdots & \vdots & \ddots & \ddots & a_n \\ 0 & 0 & \ldots & a_n & b_n \endbmatrix} |
| lexicalization | epo: Tridiagonala matrico |
| French | |
| has gloss | fra: En mathématiques, en algèbre linéaire, une matrice tridiagonale est une matrice telle que les coefficients qui ne sont pas sur la diagonale, sur la diagonale juste au-dessous ou sur la diagonale juste au-dessus sont tous nuls. |
| lexicalization | fra: matrice tridiagonale |
| Hindi | |
| lexicalization | hin: त्रिविकर्णिक आव्यूह |
| Italian | |
| has gloss | ita: In algebra lineare una matrice tridiagonale è una matrice quadrata che ha 0 ovunque fuorché sulla diagonale principale e sulle linee immediatamente al di sopra e al di sotto di essa (la prima sovradiagonale e la prima sottodiagoale). |
| lexicalization | ita: matrice tridiagonale |
| Russian | |
| has gloss | rus: Трёхдиагональной матрицей или матрицей Якоби называют матрицу следующего вида: |
| lexicalization | rus: Трехдиагональная матрица |
| lexicalization | rus: Трёхдиагональная матрица |
| Swedish | |
| has gloss | swe: En tridiagonal matris är inom matematiken en matris som är "nästan" diagonal, mer specifikt har den nollskilda element endast i huvuddiagonalen samt diagonalerna precis under och över huvuddiagonalen. |
| lexicalization | swe: tridiagonal matris |
| Chinese | |
| has gloss | zho: 性质 三对角矩阵是海森堡矩阵。尽管一般的三对角矩阵不一定是对称或埃尔米特矩阵，许多解线性代数问题时出现的矩阵却往往有这些性质。进一步如果一个实三对角矩阵 A 满足 ak,k+1 ak+1,k > 0，所以它元素的符号都为正，从而相似于一个埃尔米特矩阵，这样特征值都是实数。后一个推论如果我们将条件 ak,k+1 ak+1,k > 0 换为 ak,k+1 ak+1,k ≥ 0，结论仍然成立。 |
| lexicalization | zho: 三对角矩阵 |
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