key term - Scalar multiple
Definition
A scalar multiple is the result of multiplying a matrix by a scalar (a real number). Each element of the matrix is multiplied by the scalar to produce a new matrix.
5 Must Know Facts For Your Next Test
- Multiplying a matrix by a scalar results in each element being scaled by that number.
- The operation does not change the dimensions of the original matrix.
- Scalar multiplication is distributive, meaning $c(A+B) = cA + cB$ where $c$ is a scalar and $A$, $B$ are matrices.
- It is also associative with respect to scalar multiplication, i.e., $(ab)C = a(bC)$ where $a$ and $b$ are scalars and $C$ is a matrix.
- If you multiply any matrix by zero, the result is a zero matrix of the same dimensions.
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