June 2018
Intermediate to advanced
240 pages
9h 52m
Chinese
Content preview from Java 資料科學｜科學與工程實務方法
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線性代數 |
51
分解矩陣
考慮到我們對矩陣乘法的認識，很容易想象任何矩陣可以分解成其他矩陣。分解矩陣
可有效率且穩定的計算重要的矩陣屬性。舉例來說，雖然矩陣反轉與矩陣行列式有明
確的代數公式，但先分解矩陣然後再反轉是最好的。此行列式直接來自 Cholesky 或
LU 分解。此處使用的矩陣分解都能解決線性系統與以此反轉矩陣。表 2-1 列出 Apache
Commons Math 實作的各種矩陣分解的屬性。
表 2-1 矩陣分解屬性
分解 矩陣類型 解算 反轉 行列式
Cholesky 正定矩陣 精確
Eigen 方 精確
LU 方 精確
QR 任何 最小平方
SVD 任何 最小平方
Cholesky 分解
矩陣
A
的 Cholesky 分解使
A = LL
T
，
L
是下三角矩陣，而上三角（在對角線上）是零：
at the very least you can return a valid double such as 0.0, which is nothing more than
a placeholder. Note the method
RealMatrix.walkInOptimizedOrder(RealMatrix
ChangingVisitor visitor, int startRow, int endRow, int startColumn, int
endColumn)
, which operates only on a submatrix whose bounds are ...
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