Temperament addition: Difference between revisions

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The temperament difference can be understood as being the same operation as the temperament sum except with one of the two temperaments negated.

For single vectors (and multivectors), negation is as simple as changing the sign of every entry; for matrices, negation is accomplished by choosing a single ~~row (in~~ the ~~case~~ of ~~mappings) or column (~~in the case of comma bases) ~~and changing the sign of every entry in it~~.

For single vectors (and multivectors), negation is as simple as changing the sign of every entry; for matrices, negation is accomplished by choosing a single vector and changing the sign of every entry in it. In the case of comma bases, a vector is a column, whereas in a mapping a vector (technically a row vector, or covector) is a row.

Suppose you have a matrix representing temperament <math>T_1</math> and another matrix representing <math>T_2</math>. If you want to find both their sum and difference, you can calculate both <math>T_1 + T_2</math> and <math>T_1 + -T_2</math>. There's no need to also find <math>-T_1 + T_2</math>; this will merely give the negation of <math>T_1 + -T_2</math>. The same goes for <math>-T_1 + -T_2</math>, which is the negation of <math>T_1 + T_2</math>.

@@ Line 179: / Line 179: @@
 The temperament difference can be understood as being the same operation as the temperament sum except with one of the two temperaments negated.
-For single vectors (and multivectors), negation is as simple as changing the sign of every entry; for matrices, negation is accomplished by choosing a single row (in the case of mappings) or column (in the case of comma bases) and changing the sign of every entry in it.
+For single vectors (and multivectors), negation is as simple as changing the sign of every entry; for matrices, negation is accomplished by choosing a single vector and changing the sign of every entry in it. In the case of comma bases, a vector is a column, whereas in a mapping a vector (technically a row vector, or covector) is a row.
 Suppose you have a matrix representing temperament <math>T_1</math> and another matrix representing <math>T_2</math>. If you want to find both their sum and difference, you can calculate both <math>T_1 + T_2</math> and <math>T_1 + -T_2</math>. There's no need to also find <math>-T_1 + T_2</math>; this will merely give the negation of <math>T_1 + -T_2</math>. The same goes for <math>-T_1 + -T_2</math>, which is the negation of <math>T_1 + T_2</math>.