# Einstein Relatively Easy

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### Lorentz matrix

Another common way of expressing the Lorentz transformation is in matrix form:

Recalling the rules for matrix multiplication we see that:

We have found exacly the same Lorentz transformation equations as described in The Lorentz transformations Part I - Presentation

The two ways of expressing the equations are strictly equivalent.

We can write an even more compact form by using the index notation (see tab Index Notation)

### Index notation

We can write the Lorentz matrix in a even more compact notation, using index notation, in the form:

where the indices μ and ν take the values of the number of spacetime dimensions, ie 0 to 3.

So the components of x'μ are (x'0, x'1, x'2, x'3) = (ct', x', y', z')

And those of xμ are (x0, x1, x2, x3) = (ct, x, y, z)

Concerning the matrix,

the μ index refers to the μth row and the ν index refers to the νth column

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