Euklidsk Rom
<span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">Et </span><span style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-weight: 700; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">euklidsk rom</span><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> eller et </span><span style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-weight: 700; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">kartesisk rom</span><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> er i </span><a href="https://no.wikipedia.org/wiki/Matematikk" title="Matematikk" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">matematikk</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> et </span><a href="https://no.wikipedia.org/wiki/Reelt_tall" title="Reelt tall" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">reelt</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> endeligdimensjonalt </span><a href="https://no.wikipedia.org/wiki/Vektorrom" title="Vektorrom" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">vektorrom</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> der det er definert et såkalt euklidsk </span><a href="https://no.wikipedia.org/wiki/Indreprodukt" title="Indreprodukt" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">indreprodukt</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> og en tilhørende </span><a href="https://no.wikipedia.org/wiki/Norm_(matematikk)" title="Norm (matematikk)" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">norm</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">.</span><span class="mw-ref" id="cite_ref-DM1_1-0" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; font-size: 0.75em; line-height: 1; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: super; unicode-bidi: embed;"><a href="https://no.wikipedia.org/#cite_note-DM1-1" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161); counter-reset: mw-Ref 1;"></a></span><span class="mw-ref" id="cite_ref-WR1_2-0" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; font-size: 0.75em; line-height: 1; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: super; unicode-bidi: embed;"><a href="https://no.wikipedia.org/#cite_note-WR1-2" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161); counter-reset: mw-Ref 2;"></a></span><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> Har rommet </span><i style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">n</i><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;"> dimensjononer, betegnes det vanligvis som </span><span style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-weight: 700; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">E</span><sup style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; font-size: 0.75em; line-height: 1; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">n</sup><span style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;"> </span><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">. Definisjonen av indreproduktet medfører at euklidske rom har egenskaper som svarer til de vi er fortrolig med fra </span><a href="https://no.wikipedia.org/wiki/Euklidsk_geometri" title="Euklidsk geometri" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">Euklidsk geometri</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">. Blant annet gjelder generaliseringer av </span><a href="https://no.wikipedia.org/wiki/Pythagoras%E2%80%99_l%C3%A6resetning" title="Pythagoras’ læresetning" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">Pythagoras’ læresetning</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">og </span><a href="https://no.wikipedia.org/wiki/Parallellogramloven" title="Parallellogramloven" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; color: rgb(107, 75, 161);">parallellogramloven</a><span style="font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif;">.</span>