Douglas Blumeyer's RTT How-To: Difference between revisions

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We already have the tools to check that each of these commas’ vectors is tempered out individually by the map {{val|19 30 44}}; we learned this bit in the very first section: all we have to do is make sure that the comma maps to zero steps in this ET. But these matrices, the intersections of two of them at once, are another level of specialness. We can do even better with them. There’s actually a mathematical function which when input any one of these matrices will output {{monzo|{{val|19 30 44}}}}, thus demonstrating their equivalence with respect to it.

Remember that any one of these matrices is the null-space of {{monzo|{{val|19 30 44}}}}. So we are in effect undoing the effects of the null-space function. Interestingly enough, as you'll soon see, it's about the same process to find the null-space as it is to undo it. Working this out by hand goes like this.

Remember that any one of these matrices is the null-space of {{monzo|{{val|19 30 44}}}}. So we are in effect undoing the effects of the null-space function. Interestingly enough, as you'll soon see, it's about the same process to find the null-space as it is to undo it. Working this out by hand goes like this (it is a standard linear algebra operation, so if you're comfortable with it already, you can skip this and other similar parts of these materials):

First, transpose the matrix. That means the first column becomes the first row, the second column becomes the second row, etc.

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 We already have the tools to check that each of these commas’ vectors is tempered out individually by the map {{val|19 30 44}}; we learned this bit in the very first section: all we have to do is make sure that the comma maps to zero steps in this ET. But these matrices, the intersections of two of them at once, are another level of specialness. We can do even better with them. There’s actually a mathematical function which when input any one of these matrices will output {{monzo|{{val|19 30 44}}}}, thus demonstrating their equivalence with respect to it.
-Remember that any one of these matrices is the null-space of {{monzo|{{val|19 30 44}}}}. So we are in effect undoing the effects of the null-space function. Interestingly enough, as you'll soon see, it's about the same process to find the null-space as it is to undo it. Working this out by hand goes like this.
+Remember that any one of these matrices is the null-space of {{monzo|{{val|19 30 44}}}}. So we are in effect undoing the effects of the null-space function. Interestingly enough, as you'll soon see, it's about the same process to find the null-space as it is to undo it. Working this out by hand goes like this (it is a standard linear algebra operation, so if you're comfortable with it already, you can skip this and other similar parts of these materials):
 First, transpose the matrix. That means the first column becomes the first row, the second column becomes the second row, etc.