🧮 矩阵的秩（含行最简形）Matrix Rank Calculator
用高斯-若尔当消元求矩阵的秩，并显示行最简形（RREF）和零度（列数 - 秩）。每行一行、空格分隔。本地处理。Find the rank by Gauss-Jordan elimination, with the reduced row echelon form (RREF) and nullity (columns - rank). One row per line, space separated. Processed locally.
使用说明与常见问题How-to & FAQ
「矩阵的秩（含行最简形）」是什么？What is the Matrix Rank Calculator tool?
用高斯-若尔当消元求矩阵的秩，并显示行最简形（RREF）和零度（列数 - 秩）。每行一行、空格分隔。本地处理。Find the rank by Gauss-Jordan elimination, with the reduced row echelon form (RREF) and nullity (columns - rank). One row per line, space separated. Processed locally.
如何使用「矩阵的秩（含行最简形）」？How do I use the Matrix Rank Calculator tool?
在「矩阵的秩（含行最简形）」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 Rank Calculator: Fill in the fields above; results are recalculated instantly as you type.
秩表示什么？What does rank mean?
线性无关的行（或列）的最大个数，也是列空间的维数。The largest number of linearly independent rows (or columns) - the dimension of the column space.
计算精度如何？How precise are the results?
「矩阵的秩（含行最简形）」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 Rank Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「矩阵的秩（含行最简形）」免费吗？需要注册吗？Is the Matrix Rank Calculator free? Do I need an account?
「矩阵的秩（含行最简形）」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 Rank 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.