V2EX matrix multiplication

Matrix Multiplication

释义 Definition

矩阵乘法:一种将两个矩阵按规则相乘、得到新矩阵的运算。通常要求第一个矩阵的列数等于第二个矩阵的行数;结果矩阵的元素是对应“行向量”与“列向量”的内积之和。(在数学与工程中也常用于表示线性变换的复合。)

发音 Pronunciation (IPA)

/metrks mltplken/

例句 Examples

Matrix multiplication is not commutative.
矩阵乘法不满足交换律。

In computer graphics, matrix multiplication lets us combine rotation, scaling, and translation into a single transformation.
在计算机图形学中,矩阵乘法可以把旋转、缩放和平移合成为一个统一的变换。

词源 Etymology

matrix 源自拉丁语 matrix,原意与“母体、孕育之物”相关,后来在数学中引申为“容纳与排列数据/系数的方阵或矩形阵列”。multiplication 源自拉丁语 multiplicare(使成倍、增多)。合起来,“matrix multiplication”即“对矩阵进行成倍组合/运算的乘法”,在现代线性代数中具体化为按行列规则进行的乘法。

相关词 Related Words

文学与著作中的用例 Notable Works

  • Introduction to Linear Algebra Gilbert Strang
  • Linear Algebra Done Right Sheldon Axler
  • Matrix Computations Gene H. Golub & Charles F. Van Loan
  • The Princeton Companion to Mathematics (编)Timothy Gowers 等
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