scalar multiple

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(of a matrix)

Let A be an m×n matrix, with A=[aij], and k a scalar. The scalar multiple kA is the m×n matrix C, where C=[cij] and cij=kaij. Multiplication by scalars has the following properties:(i) (h+k)A=hA+kA.(ii)k(A+B)=kA+kB.(iii)h(kA)=(hk)A.(iv) 0A=O, the zero matrix.(v) (−1)A=−A, the negative of A.

(i) (h+k)A=hA+kA.



(iv) 0A=O, the zero matrix.

(v) (−1)A=−A, the negative of A.

Subjects: Mathematics.

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