Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Mon, 09 Jan 2023 01:08:52 -0800 Received: from [192.168.123.254] (port=55496 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1pEo9C-00FTHF-3Z for jbovlaste-admin@lojban.org; Mon, 09 Jan 2023 01:08:52 -0800 Received: by jiten.lojban.org (sSMTP sendmail emulation); Mon, 09 Jan 2023 09:08:50 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word pu'e'ei -- By krtisfranks Date: Mon, 9 Jan 2023 09:08:49 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: -2.9 (--) X-Spam_score: -2.9 X-Spam_score_int: -28 X-Spam_bar: -- In jbovlaste, the user krtisfranks has edited a definition of "pu'e'ei" in the language "English". Differences: 5,5c5,5 < For example, the span of vectors $v_1$ and $v_2$ in vector space $V$ over the field of exactly all real numbers R has $X_1 =$ Intersect$(V,$ Set$(v_1, v_2))$ and $X_2 =$ R and yields output Set$(c_1 v_1 + c_2 v_2 : c_i$ in R$)$, where scalar multiplication and vector addition are as defined in $V$. --- > For example, the span of vectors $v_1$ and $v_2$ in vector space $V$ over the field of exactly all real numbers R has $X_1 =$ Intersect$(V,$ Set$(v_1, v_2))$ and $X_2 =$ R and yields output Set$(c_1 v_1 + c_2 v_2 : c_i$ in R for all$i)$, where scalar multiplication and vector addition are as defined in $V$. Old Data: Definition: mekso binary operator: generate span; outputs span$(X_1, X_2)=$ span$_{X_2}(X_1)$; set of all (finite) sums of terms of form $c v$, where $v$ is an element of algebraic structure $X_1$ (wherein scalar multiplication and summation is defined), and $c$ is a scalar belonging to ring $X_2$. Notes: For example, the span of vectors $v_1$ and $v_2$ in vector space $V$ over the field of exactly all real numbers R has $X_1 =$ Intersect$(V,$ Set$(v_1, v_2))$ and $X_2 =$ R and yields output Set$(c_1 v_1 + c_2 v_2 : c_i$ in R$)$, where scalar multiplication and vector addition are as defined in $V$. Jargon: Gloss Keywords: Word: linear combination, In Sense: Word: linear superposition, In Sense: Word: span, In Sense: algebra Place Keywords: New Data: Definition: mekso binary operator: generate span; outputs span$(X_1, X_2)=$ span$_{X_2}(X_1)$; set of all (finite) sums of terms of form $c v$, where $v$ is an element of algebraic structure $X_1$ (wherein scalar multiplication and summation is defined), and $c$ is a scalar belonging to ring $X_2$. Notes: For example, the span of vectors $v_1$ and $v_2$ in vector space $V$ over the field of exactly all real numbers R has $X_1 =$ Intersect$(V,$ Set$(v_1, v_2))$ and $X_2 =$ R and yields output Set$(c_1 v_1 + c_2 v_2 : c_i$ in R for all$i)$, where scalar multiplication and vector addition are as defined in $V$. Jargon: Gloss Keywords: Word: linear combination, In Sense: Word: linear superposition, In Sense: Word: span, In Sense: algebra Place Keywords: You can go to to see it.