⊗ 矩阵张量积（克罗内克积）Tensor Product Calculator (Kronecker Product)
A ⊗ B：把 A 的每个元素 aᵢⱼ 换成 aᵢⱼB，得到 (m·p) × (n·q) 的矩阵。也适用于向量（单行或单列）。本地处理。A ⊗ B replaces each entry aᵢⱼ of A with aᵢⱼB, giving an (m·p) × (n·q) matrix. Works for vectors too (a single row or column). Processed locally.
使用说明与常见问题How-to & FAQ
「矩阵张量积（克罗内克积）」是什么？What is the Tensor Product Calculator (Kronecker Product) tool?
A ⊗ B：把 A 的每个元素 aᵢⱼ 换成 aᵢⱼB，得到 (m·p) × (n·q) 的矩阵。也适用于向量（单行或单列）。本地处理。A ⊗ B replaces each entry aᵢⱼ of A with aᵢⱼB, giving an (m·p) × (n·q) matrix. Works for vectors too (a single row or column). Processed locally.
如何使用「矩阵张量积（克罗内克积）」？How do I use the Tensor Product Calculator (Kronecker Product) tool?
在文本框中按行填写矩阵 A 和 B（向量写成一行或一列），即可得到张量积 A ⊗ B。结果会随输入实时更新。Type matrices A and B row by row into the boxes (a vector is a single row or column) to get the tensor product A ⊗ B. The result updates as you type.
交换律？Commutative?
一般 A ⊗ B ≠ B ⊗ A，但两者只差行列置换。In general A ⊗ B ≠ B ⊗ A, though they differ only by row and column permutations.
计算精度如何？How precise are the results?
「矩阵张量积（克罗内克积）」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 Tensor Product Calculator (Kronecker Product) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「矩阵张量积（克罗内克积）」免费吗？需要注册吗？Is the Tensor Product Calculator (Kronecker Product) free? Do I need an account?
「矩阵张量积（克罗内克积）」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 Tensor Product Calculator (Kronecker Product) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.