Extended bra–ket notation: Difference between revisions

Line 58:

RTT mappings are typically thought of in terms of their ''rows''. This mapping has two rows; let's call them <math>~~\textbf{r}_1~~</math> and <math>~~\textbf{r}_2~~</math>. And so to notate this mapping in EBK, we can first imagine capturing the rows as bras like we would normally: <math>~~\textbf{r}_1~~</math> = {{map|1 0 -4}} and <math>~~\textbf{r}_2~~</math> = {{map|0 1 4}}. Then, to put them together, we can think of this matrix as a single column containing these two rows, or in other words, a ket containing the two bras: {{ket|<math>~~\textbf{r}_1~~</math> <math>~~\textbf{r}_2~~</math>}}, or fully written out, {{ket|{{map|1 0 -4}} {{map|0 1 4}}}}.

RTT mappings are typically thought of in terms of their ''rows''. This mapping has two rows; let's call them <math>𝒓_1</math> and <math>𝒓_2</math>. And so to notate this mapping in EBK, we can first imagine capturing the rows as bras like we would normally: <math>𝒓_1</math> = {{map|1 0 -4}} and <math>𝒓_2</math> = {{map|0 1 4}}. Then, to put them together, we can think of this matrix as a single column containing these two rows, or in other words, a ket containing the two bras: {{ket|<math>𝒓_1</math> <math>𝒓_2</math>}}, or fully written out, {{ket|{{map|1 0 -4}} {{map|0 1 4}}}}.

For another example, the canonical [[comma basis]] for 7-ET consists of the two commas 2187/2048 and 135/128, with PC-vectors {{vector|-11 7}} and {{vector|-7 3 1}}, respectively. As a matrix, we'd see this as:

Revision as of 01:13, 6 March 2022 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,171 edits Created page with "'''Extended Bra-Ket notation''', or '''EBK''' for short, is a potential name for the notation system for regular temperament theory (RTT) objects that has gradually develo..."		Revision as of 19:00, 25 October 2022 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,171 edits standardizing in our articles to bold italic for maps Newer edit →
Line 58:		Line 58:


	RTT mappings are typically thought of in terms of their ''rows''. This mapping has two rows; let's call them <math>~~\textbf{r}_1~~</math> and <math>~~\textbf{r}_2~~</math>. And so to notate this mapping in EBK, we can first imagine capturing the rows as bras like we would normally: <math>~~\textbf{r}_1~~</math> = {{map\|1 0 -4}} and <math>~~\textbf{r}_2~~</math> = {{map\|0 1 4}}. Then, to put them together, we can think of this matrix as a single column containing these two rows, or in other words, a ket containing the two bras: {{ket\|<math>~~\textbf{r}_1~~</math> <math>~~\textbf{r}_2~~</math>}}, or fully written out, {{ket\|{{map\|1 0 -4}} {{map\|0 1 4}}}}.		RTT mappings are typically thought of in terms of their ''rows''. This mapping has two rows; let's call them <math>𝒓_1</math> and <math>𝒓_2</math>. And so to notate this mapping in EBK, we can first imagine capturing the rows as bras like we would normally: <math>𝒓_1</math> = {{map\|1 0 -4}} and <math>𝒓_2</math> = {{map\|0 1 4}}. Then, to put them together, we can think of this matrix as a single column containing these two rows, or in other words, a ket containing the two bras: {{ket\|<math>𝒓_1</math> <math>𝒓_2</math>}}, or fully written out, {{ket\|{{map\|1 0 -4}} {{map\|0 1 4}}}}.

	For another example, the canonical [[comma basis]] for 7-ET consists of the two commas 2187/2048 and 135/128, with PC-vectors {{vector\|-11 7}} and {{vector\|-7 3 1}}, respectively. As a matrix, we'd see this as:		For another example, the canonical [[comma basis]] for 7-ET consists of the two commas 2187/2048 and 135/128, with PC-vectors {{vector\|-11 7}} and {{vector\|-7 3 1}}, respectively. As a matrix, we'd see this as: