# Math Help - Rank and rational functions

1. ## Rank and rational functions

Suppose a matrix A (say size 6x6) has rank 2, then any diagonal element can be expressed as rational functions of certain off-diagonal elements. (Using certain 3x3 matrix determinants which are 0)

For example
a11 = ( a12(a41a53-a51a43) - a13(a41a52-a51a42) ) / ( a42a53-a52a43 )

Suppose it has rank 3, can diagonal elements be expressed as rational functions of any set of off-diagonal elements (only off-diagonal) ??

2. ## Re: Rank and rational functions

Hey srkri.

I'm not familiar with rational functions but wikipedia gives a ratio of two polynomials (which I'm sure is not what you are referring to), so could you please explain what a rational function is in your context?

3. ## Re: Rank and rational functions

I do mean rational functions as ratio of two polynomials.
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9424980282783508, "perplexity": 1196.1287233659655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207926828.58/warc/CC-MAIN-20150521113206-00260-ip-10-180-206-219.ec2.internal.warc.gz"}