Matrices of the same shape are added entry by entry. For fixed dimensions over a field, this operation and scalar multiplication make the matrices a vector space. A matrix product has a different dimension-matching rule: its inner dimensions must agree, whereas addition requires the entire shapes to agree.
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Matrix addition is a fundamental operation in linear algebra where two matrices of the same dimensions are added together element-wise. This means that corresponding entries in the two matrices are summed to produce a new matrix.