Scalar multiplication involves multiplying each entry of a matrix by a constant value, known as the scalar. This operation results in a new matrix where each element is the product of the original element and the scalar.
5 Must Know Facts For Your Next Test
Scalar multiplication is performed element-wise across the entire matrix.
If $c$ is a scalar and $A$ is an $m \times n$ matrix, then $cA$ produces another $m \times n$ matrix.
The distributive property applies: $c(A + B) = cA + cB$, where $A$ and $B$ are matrices of the same dimensions.
The associative property with respect to scalars holds: $(cd)A = c(dA)$, where $c$ and $d$ are scalars.
Multiplying a matrix by the scalar zero results in a zero matrix, where all elements are zero.