matrix multiplication

Matrix multiplication involves combining two matrices to produce a new matrix, capturing complex relationships between their elements. Imagine each row of the first matrix as a set of numbers representing a group, and each column of the second matrix as another group. To multiply, you take each row from the first matrix and compute the dot product with each column of the second matrix—multiplying corresponding elements and summing the results. The outcome is a new matrix where each element reflects how the original two matrices' data relate, often used in areas like computer graphics, data transformations, and systems of equations.