# What is the “fourth” Haar basis function of the 4×4 Haar basis?

I know the three Haar basis functions

//mother wavelet:
[1 1 -1 -1]
//dilation:
[1 -1 0 0]
//translation:
[0 0 1 -1]


However, the Haar basis consists of four basis elements: The mother wavelet, the translation, the dilation and another, fourth element, which I don't understand. According to this, this fourth element is

[1 1 1 1]


But how would this one look like, and how is it obtained (dilation/translation, whatever combination)? This confuses me.

Btw: is the Haar basis defined as

[ 1  1  1  1
1  1 -1 -1
1 -1  0  0
0  0  1 -1]


or as the transpose of this?

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