🧮 矩阵的迹Matrix Trace Calculator
方阵的迹 = 主对角线元素之和，等于全部特征值之和；同时给出主对角线元素。本地处理。The trace of a square matrix is the sum of its main-diagonal entries, which equals the sum of its eigenvalues. Processed locally.
使用说明与常见问题How-to & FAQ
「矩阵的迹」是什么？What is the Matrix Trace Calculator tool?
方阵的迹 = 主对角线元素之和，等于全部特征值之和；同时给出主对角线元素。本地处理。The trace of a square matrix is the sum of its main-diagonal entries, which equals the sum of its eigenvalues. Processed locally.
如何使用「矩阵的迹」？How do I use the Matrix Trace Calculator tool?
在文本框中按行填写方阵（每行一行数字），即可得到矩阵的迹，也就是主对角线元素之和。结果会随输入实时更新。Type the square matrix into the box, one row per line, to get its trace, the sum of the main-diagonal entries. The result updates as you type.
性质？Properties?
tr(A + B) = tr(A) + tr(B)，tr(AB) = tr(BA)。tr(A + B) = tr(A) + tr(B) and tr(AB) = tr(BA).
计算精度如何？How precise are the results?
「矩阵的迹」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 Trace Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「矩阵的迹」免费吗？需要注册吗？Is the Matrix Trace Calculator free? Do I need an account?
「矩阵的迹」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 Trace 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.