🧮 矩阵列空间（基与秩）Column Space Calculator
用行化简（RREF）找主元列，原矩阵的主元列构成列空间的一组基；同时给出秩。本地处理。Row-reduce (RREF) to find pivot columns; those columns of the original matrix form a basis of the column space. Rank is shown too. Processed locally.
使用说明与常见问题How-to & FAQ
「矩阵列空间（基与秩）」是什么？What is the Column Space Calculator tool?
用行化简（RREF）找主元列，原矩阵的主元列构成列空间的一组基；同时给出秩。本地处理。Row-reduce (RREF) to find pivot columns; those columns of the original matrix form a basis of the column space. Rank is shown too. Processed locally.
如何使用「矩阵列空间（基与秩）」？How do I use the Column Space Calculator tool?
在「矩阵列空间（基与秩）」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 Column Space Calculator: Fill in the fields above; results are recalculated instantly as you type.
为什么取原矩阵的列？Why the original columns?
行变换会改变列空间，但不改变列之间的线性关系，所以 RREF 中主元所在的列号对应原矩阵中线性无关的列。Row operations change the column space but keep the linear relations between columns, so the pivot positions in the RREF pick out independent columns of the original matrix.
计算精度如何？How precise are the results?
「矩阵列空间（基与秩）」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 Column Space Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「矩阵列空间（基与秩）」免费吗？需要注册吗？Is the Column Space Calculator free? Do I need an account?
「矩阵列空间（基与秩）」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 Column Space 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.