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I am trying to self-teach scientific German for historical purposes. A sentence in a mathematical book (1922) occurs like:

Ist nunmehr eine Darstellung Γ von höherem Grade gegeben, so läßt sich die dem Element A entsprechende Matrix transformieren auf die Form:

DeepL and Google translate it the same way:

If now a representation Γ of higher degree is given, then the matrix corresponding to the element A can be transformed to the form:

My question is with the construction, so läßt sich die dem Element A. How do we understand die and dem occurring together? To which noun is die referring to? I feel die must be a demonstrative pronoun because the verb transformieren is not in the end. What could be literal translation of the so läßt sich die dem Element A entsprechende Matrix transformieren auf die Form:?

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    This is not a construction. It is a mixture of fragments of two expressions: "so lässt sich die Matrix transformieren" (main clause) and "dem Element A entsprechende" (adjectival phrase that modifies "Matrix"). – Kilian Foth Nov 12 '18 at 7:20
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    Actually the two expressions are not only mixed but also nested. Nested expressions can be found often in German, and they are a frequent source of confusion because other European languages tend to avoid them. – RHa Nov 12 '18 at 9:42
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    I'd say nesting is one of the most prominent features of German. It's everywhere. – Janka Nov 12 '18 at 14:09
  • Could anyone provide another example of nesting with a translation? I believe this is same as participial construction. Right? – M. Farooq Nov 12 '18 at 15:00
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    Another example: Herbstlichkeit, Überlebtheit schien über dem einst so farbig belebten, nun fast verlassenen Lustorte zu liegen (Thomas Mann) – RHa Nov 12 '18 at 20:39
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Both translations are ok, although the google one is closer to the original. As for "die": it is neither demonstrative (Demonstrativpronomen) nor relative (Relativpronomen), just the definite article (bestimmter Artikel).

The whole sentence is made of two main clauses (Hauptsätze) separated by a comma. That both clauses are main clauses can be seen by the fact that both sentences do have their conjugated verb not in end position. Furthermore, "transformieren" is not the conjugated verb in the second clause, it is "lässt" a modal verb that is here combined with the indicative "transformieren".

As for the phrase "die dem Element A entsprechende Matrix":

It is similar to a relative clause: "..., so läßt sich die Matrix, die dem Element A entspricht, transformieren auf die Form:" But instead of this formulation using a relative clause, the author has used present participle (Partizip Präsens).

  • Thanks, for clarifying. With which noun is "die" associated if these are two main clauses separated by a comma because we have "so lässt die dem Element A"? Actually "die and dem" occuring together is somewhat confusing for me. I assume dem Element = to the element. – M. Farooq Nov 12 '18 at 6:26
  • Sorry, I can't follow you. What is your question? – Maximilian Nov 12 '18 at 6:38
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    "die" belongs to "Matrix" – Maximilian Nov 12 '18 at 7:16
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    The first clause is not a main clause but a subordinary clause without a conjunction (uneingeleiteter Nebensatz). – RHa Nov 12 '18 at 8:20
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    That's right, and this is the reason why the first clause cabnnot be a main clause, because in this case the verb would have to be second. In a subordinate clause without a conjunction the verb is first, and this is what we have here. – RHa Nov 12 '18 at 20:12

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