Elmentemösszegyezte

Elmentemösszegyezte, also known as element summation or element-wise addition in Hungarian, refers to the mathematical operation of adding corresponding elements of two or more vectors, matrices, or higher-dimensional arrays. This process is fundamental in linear algebra, numerical computing, and various fields of applied mathematics.

In this operation, each element of the output array is computed as the sum of the elements at the same position in the input arrays. For example, if two vectors A and B of length *n* are given, the resulting vector C will have elements calculated as C[i] = A[i] + B[i] for all indices *i* from 1 to *n*. This differs from matrix multiplication, where the dot product of rows and columns is used instead of direct element-wise addition.

Element-wise operations are widely used in computational frameworks such as NumPy (a Python library) and MATLAB, where they enable efficient manipulation of large datasets. They are particularly useful in machine learning, image processing, and scientific simulations, where arrays of numerical values are frequently processed in parallel.

The operation can be extended to more than two arrays, though the result remains a single array where each element is the sum of the corresponding elements in the input arrays. For instance, adding three vectors A, B, and C yields D[i] = A[i] + B[i] + C[i]. This method is computationally efficient and often implemented in optimized libraries to handle large-scale data processing.

Elmentemösszegyezte is also a key concept in parallel computing, as it can be easily distributed across multiple processors or cores, reducing computation time for large datasets. Its simplicity and efficiency make it a cornerstone of modern numerical algorithms.