Extended bra–ket notation: Difference between revisions
Dave Keenan (talk | contribs) →Variant including curly and square brackets: Added "This is consistent with the fact that it is common for linear algebra texts to treat a nullspace basis not as a matrix but as a mere list of vectors." |
Dave Keenan (talk | contribs) →Advantage: Replaced "more easier" with "easier". |
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EBK is capable of doing this because of how vectors and covectors are interpreted as matrices. Specifically, a vector can be thought of as a <math>(x,1)</math>-shaped matrix (many rows, one column), while a covector can be thought of as a <math>(1,x)</math>-shaped matrix (one row, many columns). | EBK is capable of doing this because of how vectors and covectors are interpreted as matrices. Specifically, a vector can be thought of as a <math>(x,1)</math>-shaped matrix (many rows, one column), while a covector can be thought of as a <math>(1,x)</math>-shaped matrix (one row, many columns). | ||
So, one way to think of a matrix would be as a single vector column which contains a number of covector rows. Another way to think of a matrix would be as a single covector row which contains a number of vector columns. Either way is possible, but in most cases, one of these two ways will be | So, one way to think of a matrix would be as a single vector column which contains a number of covector rows. Another way to think of a matrix would be as a single covector row which contains a number of vector columns. Either way is possible, but in most cases, one of these two ways will be easier to understand. | ||
====Examples==== | ====Examples==== | ||