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Question

Define a scalar matrix.

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Solution

In order to define Scalar matrix, first we should know the definition of diagonal matrix.
A Diagonal matrix is a matrix in which the entries outside the main diagonal are all zeros, which means the matrix should have non zero elements only in the diagonal running from the upper left to the lower right.
A Diagonal matrix whose diagonal elements all contains the same scalar λ is called Scalar matrix.
Therefore a scalar matrix is equivalent to λI , where I is identity matrix.

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