Editing Four-vector (section)

====Linearity====

Four-vectors have the same [[Linear algebra|linearity properties]] as [[Euclidean vector]]s in [[three dimensions]]. They can be added in the usual entrywise way:
<math display="block">\begin{align}
\mathbf{A} + \mathbf{B} &= \left(A^0, A^1, A^2, A^3\right) + \left(B^0, B^1, B^2, B^3\right) \\
&= \left(A^0 + B^0, A^1 + B^1, A^2 + B^2, A^3 + B^3\right)
\end{align}</math>
and similarly [[scalar multiplication]] by a [[scalar (mathematics)|scalar]] ''λ'' is defined entrywise by:
<math display="block">\lambda\mathbf{A} = \lambda\left(A^0, A^1, A^2, A^3\right) = \left(\lambda A^0, \lambda A^1, \lambda A^2, \lambda A^3\right)</math>

Then subtraction is the inverse operation of addition, defined entrywise by:
<math display="block">\begin{align}
\mathbf{A} + (-1)\mathbf{B} &= \left(A^0, A^1, A^2, A^3\right) + (-1)\left(B^0, B^1, B^2, B^3\right) \\
&= \left(A^0 - B^0, A^1 - B^1, A^2 - B^2, A^3 - B^3\right)
\end{align}</math>