<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="">… in exact arithmetic, not in floating-point, which is what people tend to actually use for matrices. For that matter, the entire notion of “invertible” as a binary attribute is problematic when dealing with approximate arithmetic; a matrix may be formally invertible but so ill-conditioned that the result is effectively meaningless.</div><div class=""><br class=""></div><div class="">Not really trying to shoot you down, just observing that this is an extremely subtle example with lots of hidden sharp edges.</div><div class=""><br class=""></div><div class="">– Steve</div><br class=""><div><blockquote type="cite" class=""><div class="">On Jan 13, 2016, at 1:19 PM, Matt Whiteside via swift-evolution <<a href="mailto:swift-evolution@swift.org" class="">swift-evolution@swift.org</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><span style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">That was my thinking when I wrote it, but I’m not sure exactly what the limits would be. For example, the product of 2 invertible matrices is an invertible matrix, giving you another way to construct one.</span><div class="" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;"><br class=""></div><div class="" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;">Matt</div><div class="" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;"><br class=""></div><div class="" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;"><br class=""><div class=""><blockquote type="cite" class=""><div class="">On Jan 13, 2016, at 09:56, Thorsten Seitz <<a href="mailto:tseitz42@icloud.com" class="">tseitz42@icloud.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="auto" class=""><div class=""></div><div class=""><br class=""></div><div class="">Am 12.01.2016 um 23:49 schrieb Matt Whiteside via swift-evolution <<a href="mailto:swift-evolution@swift.org" class="">swift-evolution@swift.org</a>>:<br class=""><br class=""></div><blockquote type="cite" class=""><div class="" style="margin: 0px; line-height: normal; font-family: Menlo; color: rgb(0, 132, 0);"><span class="" style="font-variant-ligatures: no-common-ligatures; color: rgb(187, 44, 162);">struct</span><span class="" style="font-variant-ligatures: no-common-ligatures;"><span class="Apple-converted-space"> </span>InvertibleMatrix:<span class="Apple-converted-space"> </span></span><span class="" style="font-variant-ligatures: no-common-ligatures; color: rgb(112, 61, 170);">SquareMatrix</span><span class="" style="font-variant-ligatures: no-common-ligatures;"><span class="Apple-converted-space"> </span></span><span class="" style="font-variant-ligatures: no-common-ligatures; color: rgb(187, 44, 162);">where</span><span class="" style="font-variant-ligatures: no-common-ligatures;"><span class="Apple-converted-space"> </span>determinant() !=<span class="Apple-converted-space"> </span></span><span class="" style="font-variant-ligatures: no-common-ligatures; color: rgb(39, 42, 216);">0</span><span class="" style="font-variant-ligatures: no-common-ligatures;"> </span></div><div class="" style="margin: 0px; line-height: normal; font-family: Menlo; color: rgb(0, 132, 0);"><span class="" style="font-variant-ligatures: no-common-ligatures;">// ^~~ 'restriction’ clause, i.e., not inheritance;</span></div><div class="" style="margin: 0px; line-height: normal; font-family: Menlo;"><span class="" style="color: rgb(0, 132, 0);">// determinant() is executed at compile time,</span></div><div class="" style="margin: 0px; line-height: normal; font-family: Menlo;"><span class="" style="color: rgb(0, 132, 0);">// since `entries` is a constexpr</span></div></blockquote><br class=""><div class="">Wouldn't that only work for literal matrices?</div><div class=""><br class=""></div><div class="">-Thorsten </div></div></div></blockquote></div><br class=""></div><img src="https://u2002410.ct.sendgrid.net/wf/open?upn=pngPxwQ4BiP5IDU2rQC6TcjbiXVR4eqjpuzmzac21kgUodl7Z8pLIQXgpWNyzri856C-2FPT1Nzvw1s4yq7B-2FbWJefbRJW1H9pqtnnzIxXGLQtelVD-2BPm4jrqWCO9Yw0LfnzzDIW6SugXGfNNh-2FWp2HP6pT28OTFaUowoQIr-2FK2o-2Bnwh6EDUxA2XeYOdnzumacz8DgqF-2BpYZZMwhFoptG3-2B4IvPv6HIgln-2BoBDlFNBrsg-3D" alt="" width="1" height="1" border="0" style="font-family: Helvetica; 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