MathAlgebraLinear algebraLinear operators

Linear operators and matrices

Combination of operators

Report a typo

Let $\mathcal{A}$ and $\mathcal{B}$ be linear operators on the same vector space $V$ . We can combine those operators into an operator $\mathcal{AB}$ by applying operator $\mathcal{B}$ first and operator $\mathcal{A}$ second. Is the following statement true or false?

"Operator $\mathcal{AB}$ is linear."

Select one option from the list

This statement is false

This statement is true

It depends on the linear operator

It depends on the vector space

___

Create a free account to access the full topic