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Matrix Direct Sum

Tool to calculate the direct sums of matrices. The direct sum calculates the sum of N matrices of different sizes.

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Matrix Direct Sum -

Tag(s) : MATRIX

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Matrix Direct Sum

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Direct Sum of 2 Matrices



Tool to calculate the direct sums of matrices. The direct sum calculates the sum of N matrices of different sizes.

Answers to Questions

How to add 2 matrices with direct sum?

Consider \( M_1=[a_{ij}] \) a matrix of \( m \) lines and \( n \) columns and \( M_2=[b_{ij}] \) a matrix of \( p \) lines and \( q \) columns.

The direct sum of these 2 matrices is noted with the character \( M_1 \oplus M_2 \) is a matrix of \( m+p \) lines and \( n+q \) columns.

$$ A \oplus B = \begin{pmatrix} [a_{ij}] & [0] \\ [0] & [b_{ij}] \end{pmatrix} $$

For example:

$$ \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix} \oplus \begin{pmatrix} 7 & 8 \\ 9 & 10 \end{pmatrix} = \begin{pmatrix} 1 & 2 & 3 & 0 & 0 \\ 4 & 5 & 6 & 0 & 0 \\ 0 & 0 & 0 & 7 & 8 \\ 0 & 0 & 0 & 9 & 10 \end{pmatrix} $$

The direct sum operation must be distinguished from the conventional operation of matrix additionhref, although it may take different size matrices, the result is not at all identical.

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