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

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# Just as a vector is the dual of a covector, we also have a '''multivector''' which is the dual of a multicovector.

# We can calculate a multivector from a comma basis matrix much in the same way we can calculate a multicovector from a mapping matrix

# We can convert between multicovectors and multivectors using an operation called “taking the '''complement'''”, which basically involves reversing the order of terms and negating some of them.

# We can convert between multicovectors and multivectors using an operation called “taking the '''complement'''”<ref>Elsewhere on the wiki you may find the complement operation called "taking [[the dual]]", or even the dual of a multicovector being called simply "the dual". An alternate name for "taking the complement" may be "taking the Hodge dual", but in these materials, I am using the dual to refer to the general case, while the specific case of the dual of a multicovector is a multivector and the operation to get from one of these to its dual is called taking the complement (whereas to get to the dual of a mapping, which is a comma basis, the operation is called taking the null-space).</ref>, which basically involves reversing the order of terms and negating some of them.

[[File:Algebra notation.png|300px|thumb|right|'''Figure 5a.''' RTT bracket notation comparison.]]

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 # Just as a vector is the dual of a covector, we also have a '''multivector''' which is the dual of a multicovector.
 # We can calculate a multivector from a comma basis matrix much in the same way we can calculate a multicovector from a mapping matrix
-# We can convert between multicovectors and multivectors using an operation called “taking the '''complement'''”, which basically involves reversing the order of terms and negating some of them.
+# We can convert between multicovectors and multivectors using an operation called “taking the '''complement'''”<ref>Elsewhere on the wiki you may find the complement operation called "taking [[the dual]]", or even the dual of a multicovector being called simply "the dual". An alternate name for "taking the complement" may be "taking the Hodge dual", but in these materials, I am using the dual to refer to the general case, while the specific case of the dual of a multicovector is a multivector and the operation to get from one of these to its dual is called taking the complement (whereas to get to the dual of a mapping, which is a comma basis, the operation is called taking the null-space).</ref>, which basically involves reversing the order of terms and negating some of them.
 [[File:Algebra notation.png|300px|thumb|right|'''Figure 5a.''' RTT bracket notation comparison.]]