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In this note we answer this question for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n times n\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u00d7\n                              \n                            <\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n \\times n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    matrices, giving a solution that is exact to first-order as\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n right-arrow normal infinity\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo stretchy=\"false\">\n                              \u2192\n                              \n                            <\/mml:mo>\n                            <mml:mi mathvariant=\"normal\">\n                              \u221e\n                              \n                            <\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n \\rightarrow \\infty<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/mcom\/3706","type":"journal-article","created":{"date-parts":[[2021,10,27]],"date-time":"2021-10-27T09:41:22Z","timestamp":1635327682000},"page":"1237-1245","source":"Crossref","is-referenced-by-count":0,"title":["How well-conditioned can the eigenvector problem be?"],"prefix":"10.1090","volume":"91","author":[{"given":"Carlos","family":"Beltr\u00e1n","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"B\u00e9termin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Grabner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Steinerberger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2021,12,7]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/j.laa.2004.10.013","article-title":"On sensitivity of eigenvalues and eigendecompositions of matrices","volume":"396","author":"Alam, R.","year":"2005","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"issue":"6","key":"2","doi-asserted-by":"publisher","first-page":"1375","DOI":"10.4171\/JEMS\/789","article-title":"A stable, polynomial-time algorithm for the eigenpair problem","volume":"20","author":"Armentano, Diego","year":"2018","journal-title":"J. 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