While a state vector should be given as a row vector, we will use the transpose of the matrix so that the calculations below are easier to read.
22.
If = 1, is a scalar field and the Jacobian matrix is reduced to a row vector of partial derivatives of i . e . the gradient of.
23.
As a linear transformation, a lower shift matrix shifts the components of a row vector one position to the right, with a zero appearing in the first position.
24.
Specifically, am I correct in believing that a distribution is represented by a row vector and shows the status of a Markov process after some number of transition steps?
25.
Matrices which have a single row are called " row vectors ", and those which have a single column are called " column vectors ".
26.
Both of these conventions are possible even when the common assumption is made that vectors should be treated as column vectors when combined with matrices ( rather than row vectors ).
27.
In matrix notation, where } } and } } are Grassmann-valued row vectors, and are Grassmann-valued column vectors, and is a real-valued matrix:
28.
Since row operations can affect linear dependence relations of the row vectors, such a basis is instead found indirectly using the fact that the column space of " A"
29.
In order to do this, however, it is necessary to discuss how the space of spinors ( column vectors ) may be identified with its dual ( row vectors ).
30.
:: In particular if you multiply a column vector by a row vector, the resulting matrix will always have talk ) 05 : 51, 24 May 2012 ( UTC)
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