If I understand correctly, only 大きくない can be used?

e.g., 猫は大きくない, not 猫は大きじゃない?
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question
adjectives
大きじゃない vs 大きくない？
Yes. If you say "it is not big", you say "大きくない" in Japanese. 大きじゃない is wrong.
And you can say "大きくはない".
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When the adjective 大きい is negated, it becomes 大きくない.

* * *

Although the word 大きな also exists, you can't replace the な on the end with
copula forms like で or だ:

> 大き **な** 猫 'large cat'
>
> ＊大き **だ** ← _ungrammatical_  
>  ＊大き **で** はない ← _ungrammatical_  
>  ＊大き **じゃ** ない ← _ungrammatical_

This is different from most _na_ -adjectives:

> きれい **な** 花 'pretty flower'
>
> きれい **だ** ← _grammatical_  
>  きれい **で** はない ← _grammatical_  
>  きれい **じゃ** ない ← _grammatical_

So even though it ends in な, we have to be careful not to treat this word as a
normal _na_ -adjective.

* * *

This word isn't classified as a 形容動詞 ( _na_ -adjective) in most monolingual
dictionaries. Instead, it's usually classified as a
[連体詞](http://ja.wikipedia.org/wiki/%E9%80%A3%E4%BD%93%E8%A9%9E) (adnominal
word). This is a class of non-inflecting words that appear before nouns,
including words like この and とある.

However,
[Daijirin](http://www.excite.co.jp/dictionary/japanese/?search=%E5%A4%A7%E3%81%8D%E3%81%AA&match=beginswith&itemid=DJR_ookina_-010)
points out that 連体詞 generally can't function predicatively, while 大きな can:

> 耳の大きな人 ← 耳の大きな is a relative clause in which 大きな predicates on 耳

So it may make more sense to classify it as a special kind of 形容動詞 instead,
one with a restricted distribution (or set of forms). Either way, though, it's
a bit exceptional, so just keep in mind that this word is special and doesn't
fit perfectly into any category.

* * *

In this answer, the ＊ symbol means 'ungrammatical.'
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answer