# Unitary transformation

by Amith2006
Tags: transformation, unitary
 P: 423 Can it be said that similarity transformation is a transformation in real space while unitary transformation is a transformation in complex space?
 P: 1,705 lol what? an orthonormal transformation is a similarity transformation in real space. a unitary transformation is a similarity transformation in complex space. they're really the same thing, it's just that a unitary transformation is one that preserves lengths of complex numbers, which can be viewed as vectors on an argand diagram, while an orthonormal transformation preserves lengths of real vectors.
P: 423
 Quote by ice109 they're really the same thing, it's just that a unitary transformation is one that preserves lengths of complex numbers, which can be viewed as vectors on an argand diagram, while an orthonormal transformation preserves lengths of real vectors.
Since a unitary transformation preserves lengths and angle between the complex numbers in the 2 basis, doesn't it make sense to say its operates in a complex space?

P: 1,705
Unitary transformation

 Quote by Amith2006 Since a unitary transformation preserves lengths and angle between the complex numbers in the 2 basis, doesn't it make sense to say its operates in a complex space?
in a complex space? i would say it operates on a complex space.
{"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": 0.970860481262207, "perplexity": 388.74763094584847}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "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-2014-23/segments/1406510260734.19/warc/CC-MAIN-20140728011740-00412-ip-10-146-231-18.ec2.internal.warc.gz"}