🧮 矩阵幂 AⁿMatrix Power Calculator

使用说明与常见问题How-to & FAQ

「矩阵幂 Aⁿ」是什么？What is the Matrix Power Calculator tool?

用快速幂计算方阵的 n 次幂（n = 0-1000），每行一行、空格分隔输入矩阵。本地处理。Raise a square matrix to the power n (0-1000) by repeated squaring; enter one row per line, space separated. Processed locally.

如何使用「矩阵幂 Aⁿ」？How do I use the Matrix Power Calculator tool?

在「矩阵幂 Aⁿ」中，填写「指数 n」等参数，结果会随输入实时计算并显示在下方。In the Matrix Power Calculator: Fill in "Power n"; results are recalculated instantly as you type.

n = 0？n = 0?

任何方阵的 0 次幂都是单位矩阵。Any square matrix to the power 0 is the identity.

能举个计算实例吗？Can you show a worked example?

例如在「矩阵幂 Aⁿ」中填 指数 n = 10，结果区显示：A^10：89 55 55 34；精度：精确（双精度范围内）For example, entering Power n = 10 in the Matrix Power Calculator gives: A^10: 89 55 55 34; Precision: exact (within double precision)

哪些输入会被检查？Which inputs are validated?

「矩阵幂 Aⁿ」会检查这些输入——「指数 n」：必须填写，不能为负数，须为整数；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Matrix Power Calculator checks its inputs — "Power n": required, cannot be negative, must be a whole number; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「矩阵幂 Aⁿ」的设置：「指数 n」默认 10。每次生成结果都按当前设置处理。Settings in the Matrix Power Calculator — "Power n" default 10. The result always uses the current settings.

计算精度如何？How precise are the results?

「矩阵幂 Aⁿ」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 Power Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「矩阵幂 Aⁿ」免费吗？需要注册吗？Is the Matrix Power Calculator free? Do I need an account?

「矩阵幂 Aⁿ」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 Power 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.