Short Answer

Dimensionality of Concatenated Matrices

Consider the matrix C\mathbf{C} formed by the horizontal concatenation of NN matrices, A1,A2,...,AN\mathbf{A}_1, \mathbf{A}_2, ..., \mathbf{A}_N, represented as C=[A1A2...AN]\mathbf{C} = [\mathbf{A}_1 \mathbf{A}_2 ... \mathbf{A}_N]. If each matrix Ai\mathbf{A}_i has dimensions m×nim \times n_i, what are the dimensions of the resulting matrix C\mathbf{C}? Explain the reasoning behind both the row and column dimensions of the final matrix.

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Updated 2025-10-04

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