Hadamard積計算器：逐元素相乘

The Hadamard product is the simplest way to multiply two vectors or matrices when you want corresponding entries to interact directly. Instead of combining rows and columns the way standard matrix multiplication does, the Hadamard product pairs the first value with the first value, the second with the second, and so on. For vectors A = [a1, a2, a3] and B = [b1, b2, b3], the result is [a1×b1, a2×b2, a3×b3]. This calculator focuses on that exact operation for one-dimensional vectors. Element-wise multiplication appears everywhere once you start looking for it. In statistics and data science, it is used when scaling feature vectors or applying weights to observations. In signal processing, it can represent point-by-point modulation of sampled data. In machine learning, the Hadamard product shows up in attention masks, gating mechanisms, and neural-network operations where one vector selectively amplifies or suppresses another. In finance, you might use it to multiply unit holdings by per-asset returns or prices to inspect contribution by position before summing anything. One important detail is that the two vectors must have the same length. Because each output entry needs one value from the first vector and one value from the second vector, there must be a perfect one-to-one pairing across the whole sequence. If one vector has four values and the other has three, the operation is undefined. That is why the calculator validates matching lengths before producing a result. This is also a good place to distinguish the Hadamard product from the dot product. A dot product multiplies corresponding entries and then adds the products to produce a single scalar. The Hadamard product stops one step earlier and returns the full vector of pairwise products. If you later want the dot product, you could sum the entries of the Hadamard result. Keeping the intermediate vector is useful because it shows how each position contributes. Because the inputs accept comma-separated or space-separated numbers, you can paste values from spreadsheets, notes, or code with minimal cleanup. Use the tool whenever you need a fast, transparent way to inspect element-wise multiplication without writing a script or opening a larger numerical package.