49 lines
1.6 KiB
Markdown
49 lines
1.6 KiB
Markdown
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---
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title: How to Multiply Matrices
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localeTitle: 如何乘以矩阵
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---
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## 如何乘以矩阵
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第一个重要的规则是:矩阵A中的列数必须与B列中的行数匹配。
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计算两个矩阵乘积的第二个规则是:X行列。
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![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Matrix_multiplication_principle.svg/320px-Matrix_multiplication_principle.svg.png)
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得到的矩阵维度将是第二矩阵的第一矩阵X列的行。
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设A和B为维2的两个矩阵,即2 X 2.他们的产品将是:
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![](http://www.i-programmer.info/images/stories/News/2011/DEC/A/matrix1.jpg)
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resuting矩阵的行是第一矩阵行元素乘以第二矩阵列元素的乘积之和。
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#### 例
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设A为2×3矩阵,B为3×2矩阵。产品AB将是:
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* **步骤1**
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![](http://www.mathportal.org/linear-algebra/matrices/matrix-operations_files/12.gif)
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* **第2步**
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![](http://www.mathportal.org/linear-algebra/matrices/matrix-operations_files/13.gif)
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* **第3步**
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![](http://www.mathportal.org/linear-algebra/matrices/matrix-operations_files/14.gif)
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* **第4步**
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![](http://www.mathportal.org/linear-algebra/matrices/matrix-operations_files/15.gif)
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#### 注意!
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与实数代数不同,乘积AB并不总是等于BA。使用上面的例子计算它并找出答案。
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#### 更多信息:
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![关于矩阵乘法的讲座](https://www.khanacademy.org/math/precalculus/precalc-matrices/multiplying-matrices-by-matrices/v/matrix-multiplication-intro)
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![矩阵乘法的性质](https://www.khanacademy.org/math/precalculus/precalc-matrices/properties-of-matrix-multiplication/a/properties-of-matrix-multiplication)
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