× 矩阵乘法Matrix Multiply
计算两个矩阵的乘积 A×B，整数、小数和分数都精确计算。在上方输入框写 A，空一行再写 B；或者把 B 写进「矩阵 B」（用分号分行）。本地处理。Multiply two matrices, A×B, with integers, decimals and fractions computed exactly. Type A in the box above, then a blank line and B; or put B in the Matrix B field (rows separated by semicolons). Processed locally.
使用说明与常见问题How-to & FAQ
「矩阵乘法」是什么？What is the Matrix Multiply tool?
计算两个矩阵的乘积 A×B，整数、小数和分数都精确计算。在上方输入框写 A，空一行再写 B；或者把 B 写进「矩阵 B」（用分号分行）。本地处理。Multiply two matrices, A×B, with integers, decimals and fractions computed exactly. Type A in the box above, then a blank line and B; or put B in the Matrix B field (rows separated by semicolons). Processed locally.
如何使用「矩阵乘法」？How do I use the Matrix Multiply tool?
在「矩阵乘法」中，把内容粘贴或输入到上方输入框，按需设置「矩阵 B（可选，用分号分行，如 5 6; 7 8）」、「显示」，结果会实时显示在下方，点击「复制结果」即可复制。In the Matrix Multiply: Paste or type into the input box, adjust "Matrix B (optional; rows separated by semicolons, e.g. 5 6; 7 8)", "Show as"; the result appears below instantly — click "Copy result" to copy it.
如何输入两个矩阵？How do I enter the two matrices?
在上方输入框写矩阵 A（每行一行，数之间用空格或逗号），空一行，再写矩阵 B；或者只在输入框写 A，把 B 填进「矩阵 B」，行与行之间用分号，如 5 6; 7 8。两处都给了 B 时会提示，而不是悄悄选一处。Type matrix A in the box above (one row per line, numbers separated by spaces or commas), leave a blank line, then type matrix B. Or type only A in the box and put B in the Matrix B field, separating rows with semicolons, e.g. 5 6; 7 8. If B is given in both places you get a message instead of one being silently ignored.
大整数和小数精确吗？Are big integers and decimals exact?
精确。每个数都按精确有理数读入（整数、小数、1e20 这类科学计数、1/3 这类分数都可以），乘法和加法全程用大整数（BigInt）计算，不经过浮点，所以 10^20 量级的整数相乘也会得到每一位都正确的结果。显示为小数时，非有限小数会四舍五入到 12 位有效数字并在下方注明；选「分数」可看精确值。Yes. Every number is read as an exact rational (integers, decimals, scientific notation such as 1e20 and fractions such as 1/3 all work), and all multiplication and addition use big integers (BigInt) with no floating point, so even products of 10^20-sized integers come out correct to the last digit. In decimal display, non-terminating values are rounded to 12 significant digits with a note below; choose Fractions for exact values.
输入和输出是什么样的？What does the input and output look like?
例如在「矩阵乘法」中输入 1 2 ⏎ 3 4 ⏎ ⏎ 5 6 ⏎ 7 8，输出为：19 22 ⏎ 43 50（⏎ 表示换行）。For example, the Matrix Multiply turns the input 1 2 ⏎ 3 4 ⏎ ⏎ 5 6 ⏎ 7 8 into: 19 22 ⏎ 43 50 (⏎ marks a line break).
有哪些选项可以调整？What options can I adjust?
「矩阵乘法」的设置：「矩阵 B（可选，用分号分行，如 5 6; 7 8）」可留空；「显示」可选 小数、分数（精确）（默认 小数）。每次生成结果都按当前设置处理。Settings in the Matrix Multiply — "Matrix B (optional; rows separated by semicolons, e.g. 5 6; 7 8)" optional; "Show as": Decimals, Fractions (exact) (default Decimals). The result always uses the current settings.
「矩阵乘法」免费吗？需要注册吗？Is the Matrix Multiply free? Do I need an account?
「矩阵乘法」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 Multiply is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.