matt
weak
To feel physically weak, powerless, and without energy, often as a result of illness or exertion.
Nach der Grippe fühlte sie sich noch tagelang matt und müde.
After the flu, she still felt weak and tired for days.

weak / matte
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weak
To feel physically weak, powerless, and without energy, often as a result of illness or exertion.
Nach der Grippe fühlte sie sich noch tagelang matt und müde.
After the flu, she still felt weak and tired for days.

To express physical weakness, 'matt' (weak) is often used in the combination 'sich matt fühlen' (to feel weak) or as part of 'matt und müde' (weak and tired). It describes a state of lacking energy.
Ich fühle mich heute irgendwie matt und antriebslos.
I feel somehow weak and listless today.
When 'matt' (matte) describes a surface, it is always about the absence of shine. Typical nouns in this context are 'Farbe' (paint), 'Lack' (varnish/lacquer), 'Papier' (paper), or 'Foto' (photo).
Für das Porträt hat der Fotograf mattes Papier verwendet.
The photographer used matte paper for the portrait.
The meaning 'Schachmatt' (checkmate) is reserved exclusively for the game of chess. You can recognize it immediately from the context with words like 'König' (king), 'Zug' (move), 'Partie' (game), or 'Schach' (chess).
Nach nur zwanzig Zügen war der Weltmeister matt.
After only twenty moves, the world champion was checkmated.
In a chess context, there are two typical constructions: You can say 'Der König ist matt' (The king is in checkmate) as a state, or use the verb 'jemanden matt setzen' (to checkmate someone) for an action.
Sie hat ihn mit einem überraschenden Zug matt gesetzt.
She checkmated him with a surprising move.
When 'matt' (muted) describes a color, it stands directly before the color name. It then means 'not bright' or 'subdued'. Examples are 'ein mattes Grün' (a muted green) or 'ein mattes Blau' (a muted blue).
Die Bluse hatte ein mattes Rosa, das sehr elegant wirkte.
The blouse had a muted pink that looked very elegant.
tired
'müde' and 'matt' can both describe someone having little energy. 'müde' is used especially when you want to sleep or rest. 'matt' emphasizes physical weakness and lack of strength, often after illness, heat, or great exertion. So you can be 'müde' because it is late. You are more likely to be 'matt' when your body feels weak.

Nach dem Fieber ist Sofia noch matt und bleibt lieber im Bett.
After the fever, Sofia is still weak and prefers to stay in bed.
Nach der Prüfung war der Lehrer müde und wollte früh nach Hause.
After the exam, the teacher was tired and wanted to go home early.