Scalar

Definition

A scalar is a single number that can multiply a matrix, affecting all its elements equally. It is often used in operations involving matrices.

5 Must Know Facts For Your Next Test

1. Multiplying a matrix by a scalar involves multiplying each element of the matrix by that scalar.
2. Scalar multiplication does not change the dimensions of the matrix.
3. In matrix equations, scalars can simplify expressions and are crucial in solving systems of linear equations.
4. Scalars can be real numbers or complex numbers depending on the context of the problem.
5. When dealing with matrices, common operations like addition and subtraction do not involve scalars directly, but scalar multiplication is fundamental.

Review Questions

• What happens to each element of a matrix when it is multiplied by a scalar?
• Does scalar multiplication affect the dimensions of a matrix? Explain your answer.
• How does multiplying a matrix by a scalar help in solving systems of linear equations?

Related terms

Matrix:

An array of numbers arranged in rows and columns used to represent linear transformations and solve systems of equations.

Determinant:

A value calculated from a square matrix that indicates whether the system has unique solutions.

Eigenvalue:

$\lambda$ such that $Av = \lambda v$, where $A$ is a square matrix and $v$ is an eigenvector. Scalars can be eigenvalues in specific contexts.