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I have a 2-level list in the form of a $m\times n$ matrix: {{a11,a12,a13,...,a1n},{a21,a22,a23,...,a2n}, ..., {am1,am2,am3,...,amn}}, in which the numbers are normally decimals. Now, I need to compare each element in the $(n+1)$-th level to the corresponding element in the $n$-th level (i.e., the previous level). If the element in the $(n+1)$-th level is larger than that of the $n$-th level, it gives a $+$ sign; if the absolute of the difference between the two numbers is smaller than a small value, say, $0.001$, it gives a $=$ sign; otherwise a $-$ sign. The comparison should be carried out up to the last sub-list to generate a "$+/-/=$" sign table in a $(m-1)\times n$ matrix from finally.

For example, given a list of lists:

{{1.1, 2.3 ,3.4, 4.3, 5.01},{2.1, 1.2, 2.5, 5.6, 5.001},{1.2, 1.201, 1.2, 6.3, 3.7}}

Supposing a function will do the job. After the above manipulation, the desired function should give the following $2\times 5$ matrix {{+,-,-,+,=}, {-,=,-,+,-}}.

Can somebody please help me to do this with MMA. Thank you in advance.

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You can use Differences + Clip

 Clip[Differences[lst], {-.01, .01}, {"-", "+"}] /. _?NumericQ -> "="

{{"+", "-", "-", "+", "="}, {"-", "=", "-", "+", "-"}}

Alternatively, Differences + Chop + Sign

rule = {1 -> "+", -1 -> "-", 0 -> "="};

Sign[Chop[Differences[lst], .01]] /. rule

{{"+", "-", "-", "+", "="}, {"-", "=", "-", "+", "-"}}

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