How do Vectors transform from one inertial reference frame to another inertial reference frame in special relativity.

A bound vector in an inertial reference frame ($x$,$ct$) has its line of action as one of the space axis in that frame and is described by $x$*$i$*,then what would it be in form of new base vectors ($\mathbf{a}$) and ($\mathbf{b}$) in a different inertial system ($x\u2018$,$ct\u2018$) moving with respect to the former inertial system with v*i* velocity.Let (i) and (j) be the two bounded unit vectors with the line of action as co-ordinate axis($x$) and ($ct$) respectively and senses in the positive side of co-ordinates and similarly ($\mathbf{a}$) and ($\mathbf{b}$) are defined for co-ordinates ($x\u2018$) and ($ct\u2018$) respectively.

A bound vector in an inertial reference frame ($x$,$ct$) has its line of action as one of the space axis in that frame and is described by $x$*$i$*,then what would it be in form of new base vectors ($\mathbf{a}$) and ($\mathbf{b}$) in a different inertial system ($x\u2018$,$ct\u2018$) moving with respect to the former inertial system with v*i* velocity.Let (i) and (j) be the two bounded unit vectors with the line of action as co-ordinate axis($x$) and ($ct$) respectively and senses in the positive side of co-ordinates and similarly ($\mathbf{a}$) and ($\mathbf{b}$) are defined for co-ordinates ($x\u2018$) and ($ct\u2018$) respectively.