Matrisenummeret står ved katalognummeret.

Because they are in the definite singular form: the matrix number and the catalog number.

In Norwegian, the is usually added to the end of the noun instead of being a separate word.
The base noun is nummer (number), which is a neuter noun, so the definite ending is -et:

• et nummer = a number
• nummeret = the number

Since both words are compounds ending in -nummer, they follow the same pattern:

• et matrisenummer → matrisenummeret
• et katalognummer → katalognummeret

Norwegian usually puts definiteness directly on the noun as a suffix.

So instead of saying something like the matrix number, Norwegian often says:

• matrisenummeret

This is one of the biggest differences from English.
English uses a separate article (the), while Norwegian often attaches the definite ending to the noun itself.

Yes, står literally means stands, from the verb å stå (to stand). But in this sentence it is being used in a more natural Norwegian way.

Here, står means something like:

• is written
• appears
• is found
• is located

So the sentence is not saying the number is physically standing upright. It means the matrix number appears next to the catalog number.

This kind of usage is very common in Scandinavian languages when talking about words, text, labels, signs, and printed information.

Norwegian often prefers more concrete location verbs where English would simply use is.

So instead of a plain equivalent of is next to, Norwegian may say:

• står ved = stands by / is next to
• especially for something written, printed, or displayed

This sounds natural in Norwegian. English is often more abstract here, while Norwegian tends to use verbs like:

• stå = stand
• ligge = lie
• sitte = sit

depending on how something is positioned or presented.

Ved usually means:

• by
• next to
• beside
• sometimes at

In this sentence, ved katalognummeret means next to the catalog number.

So ved tells you the location of the matrix number relative to the catalog number.

This is normal Norwegian main-clause word order:

• Subject: Matrisenummeret
• Verb: står
• Adverbial / location phrase: ved katalognummeret

So it follows the basic pattern:

• Subject + verb + rest

That is very similar to English here:

• The matrix number
  • stands/is
    • by the catalog number

Also, Norwegian main clauses normally keep the finite verb in the second position, which this sentence does.

The dictionary form is å stå, which means to stand.

Some common forms are:

• å stå = to stand
• står = stands / is standing
• stod = stood
• har stått = has stood

In this sentence, står is the present tense.

Yes. Norwegian forms compound nouns very freely, and these are good examples.

• matrise + nummer → matrisenummer
• katalog + nummer → katalognummer

The last part of the compound usually determines the grammatical gender and inflection. Since nummer is neuter, the whole compound behaves as a neuter noun:

• et matrisenummer

• matrisenummeret

• et katalognummer
• katalognummeret

Yes, literally by the catalog number is possible, but in natural English next to the catalog number is usually clearer.

So:

• ved katalognummeret = by the catalog number
• more naturally: next to the catalog number

The best translation depends on context, but next to often captures the meaning well.

It would not always be impossible, but står ved is more natural here.

er ved can mean is by / is at, but it is less idiomatic when talking about information printed or written somewhere.
With text, labels, and printed details, Norwegian often uses står because the information is there in writing.

So in this sentence, står ved katalognummeret is the better and more natural choice.

Then you would remove the definite ending -et:

• Et matrisenummer står ved et katalognummer.

Grammatically, that means:

• A matrix number is next to a catalog number

But that sounds much less natural in most contexts, because the original sentence is probably referring to specific information on a record, label, or listing. That is why the definite forms matrisenummeret and katalognummeret make more sense here.