It's a bit incorrect to use term "wave of matter", it's wave of possibility and nothing more, another interpretations can cause wrong understating and paradoxes, matter looks exactly like in classical understanding and has sizes exactly like in classical predictions, electron is spherical and has certain radius and doesn't look like wave.

You can use Fourier transformation to decompose the wave to monochromatic 3D waves https://en.wikipedia.org/wiki/Sinusoidal_plane_wave, monochromatic waves have infinite "side sizes", as you said, like waves on the beach.

But you have to consider the quantum effects that limit monochromaticity of real wave functions. Our space is continuous and the price of that is the impossibility of creating ideal monochromatic waves in nature (the diffraction phenomena) Applying measurement postulate to a continuous sum of eigenvectors (by analogy)

So, our wave packet must have some different wavelengths and it localizes the particle in some place in average, it's no more the infinite everywhere the same wave: https://upload.wikimedia.org/wikipedia/commons/b/b7/Wavepacket-a2k4-en.gif

The minimum sizes of this wave packet are also limited by uncertainty_principle, where $$\Delta p\cdot\Delta x \geq \hbar/2$$ And this works in every dimension, not only in direction of particle velocity. So max side sizes of wave are not limited, but can't be infinite.

It's a bit incorrect to use term "wave of matter", it's wave of possibility and nothing more, another interpretations can cause wrong understating and paradoxes, matter looks exactly like in classical understanding and has sizes exactly like in classical predictions, electron is spherical and has certain radius and doesn't look like wave.

You can use Fourier transformation to decompose the wave to monochromatic 3D waves https://en.wikipedia.org/wiki/Sinusoidal_plane_wave, monochromatic waves have infinite "side sizes", as you said, like waves on the beach.

But you have to consider the quantum effects that limit monochromaticity of real wave functions. Our space is continuous and the price of that is the impossibility of creating ideal monochromatic waves in nature (the diffraction phenomena) Applying measurement postulate to a continuous sum of eigenvectors (by analogy)

So, our wave packet must have some different wavelengths and it localizes the particle in some place in average, it's it's no longer the infinite everywhere the same sinusoidal wave: http://31.media.tumblr.com/7cb79638bd5cc6f70ddc1851b04e2f17/tumblr_mi5zsmKUBh1rg05iho1_1280.gif

The minimum sizes of this wave packet are also limited by uncertainty_principle, where $$\Delta p\cdot\Delta x \geq \hbar/2$$ And this works in every dimension, not only in direction of particle velocity. So max side sizes of wave are not limited, but can't be infinite.