🔢 矩阵乘法计算器Matrix Multiplication Calculator
输入两个矩阵（每行一行，元素用空格或逗号分隔），计算矩阵乘积 A × B，检查维数是否匹配，并可显示每个元素的计算过程。Multiply two matrices — one row per line, entries separated by spaces or commas — to get A × B, with a dimension check and the working for each entry.
使用说明与常见问题How-to & FAQ
「矩阵乘法计算器」是什么？What is the Matrix Multiplication Calculator tool?
输入两个矩阵（每行一行，元素用空格或逗号分隔），计算矩阵乘积 A × B，检查维数是否匹配，并可显示每个元素的计算过程。Multiply two matrices — one row per line, entries separated by spaces or commas — to get A × B, with a dimension check and the working for each entry.
如何使用「矩阵乘法计算器」？How do I use the Matrix Multiplication Calculator tool?
在「矩阵乘法计算器」中，填写上方字段等参数，结果会随输入实时计算并显示在下方。In the Matrix Multiplication Calculator: Fill in the fields above; results are recalculated instantly as you type.
矩阵乘法规则？What is the rule?
A 为 m×n、B 为 n×p 时，A × B 为 m×p，元素 cᵢⱼ = Σₖ aᵢₖ·bₖⱼ（A 的第 i 行与 B 的第 j 列对应相乘再求和）。A 的列数必须等于 B 的行数。If A is m × n and B is n × p, A × B is m × p with cᵢⱼ = Σₖ aᵢₖ·bₖⱼ — row i of A times column j of B. A's column count must equal B's row count.
A × B 等于 B × A 吗？Is A × B the same as B × A?
一般不相等，矩阵乘法不满足交换律；有时 B × A 甚至因维数不匹配而无法计算。Generally not — matrix multiplication is not commutative, and B × A may not even be defined.
计算精度如何？How precise are the results?
「矩阵乘法计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Matrix Multiplication Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「矩阵乘法计算器」免费吗？需要注册吗？Is the Matrix Multiplication Calculator free? Do I need an account?
「矩阵乘法计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Matrix Multiplication Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.