V2EX hadamard product

Hadamard Product

定义 Definition

Hadamard product(阿达马乘积/哈达玛积)指两个同型矩阵(或同维向量)进行对应元素逐项相乘得到的新矩阵(或向量)。常记作 \(A \circ B\)
(注:在不同领域里也可能见到更宽泛的“逐元素乘法”用法。)

发音 Pronunciation (IPA)

/hdmrd prdkt/(美式常见)
/hdmd prdkt/(英式常见)

例句 Examples

Let \(C = A \circ B\) be the Hadamard product of two matrices of the same size.
设 \(C = A \circ B\) 为两个同型矩阵的 Hadamard product(逐元素乘积)。

In attention mechanisms, the model may use a Hadamard product to gate features by multiplying an activation vector element-wise with a learned mask.
在注意力机制中,模型可能用 Hadamard product 将激活向量与学习到的掩码逐元素相乘,以实现对特征的门控。

词源 Etymology

“Hadamard”来自法国数学家 Jacques Hadamard(雅克阿达马)的姓氏;“product”意为“乘积”。该术语用来指代一种与矩阵乘法不同的、按元素对应相乘的运算,因此又常被直观地称为 strong>element-wise product(逐元素乘法)。

相关词 Related Words

文学与著作中的用例 Literary & Notable Works

  • Roger A. Horn & Charles R. Johnson, Matrix Analysis(矩阵分析经典教材;讨论Schur/Hadamard乘积及相关性质)
  • Gene H. Golub & Charles F. Van Loan, Matrix Computations(矩阵计算权威教材;涉及逐元素运算与相关矩阵结构)
  • Thomas M. Cover & Joy A. Thomas, Elements of Information Theory(信息论经典;在相关矩阵/逐元素操作与推导中常见符号与概念关联)
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