Examples of row equivalent in the following topics:
-
- Two matrices are row equivalent if one can be changed to the other by a sequence of elementary row operations.
- In linear algebra, two matrices are row equivalent if one can be changed to the other by a sequence of elementary row operations.
- Alternatively, two $m \times n$matrices are row equivalent if and only if they have the same row space.
- Two matrices of the same size are row equivalent if and only if the corresponding homogeneous systems have the same set of solutions, or equivalently the matrices have the same null space.
- Because elementary row operations are reversible, row equivalence is an equivalence relation.
-
- If you have a matrix that can be derived from another matrix by a sequence of elementary operations, then the two matrices are said to be row or column equivalent.
- because we can add 2 times row 3 of A to row 2 of A; then interchange rows 2 and 3; finally multiply row 1 by 2.
- The first is the application of elementary operations to try to put the matrix in row-reduced form; i.e., making zero all the elements below the main diagonal (and normalizing the diagonal elements to 1).
- Unless the matrix is very simple, calculating any of the four fundamental subspaces is probably easiest if you put the matrix in row-reduced form first.
-
- But, even more generally, we can see that two actors are structurally equivalent to extent that the profile of scores in their rows and columns are similar.
- Finding automorphic equivalence and regular equivalence is not so simple.
- This means that the entries in the rows and columns for one actor are identical to those of another.
- If the matrix were symmetric, we would need only to scan pairs of rows (or columns).
- Concatenated row and column adjacencies for Knoke information network
-
- Table 1.35 shows the row proportions for Table 1.32.
- The row proportions are computed as the counts divided by their row totals.
- We could also have checked for an association between spam and number in Table 1.35 using row proportions.
- Example 1.41 points out that row and column proportions are not equivalent.
- A contingency table with row proportions for the spam and number variables.
-
- For larger graphs, direct search for all equivalencies is impractical both because it is computationally intensive, and because exactly equivalent actors are likely to be rare.
- That is, the algorithm seeks to group together actors who have similar amounts of variability in their row and column scores within blocks.
- The newspaper (actor 7) has low rates of sending (row) and high rates of receiving (column); the mayor (actor 5) has high rates of sending and high rates of receiving.
- This goes beyond structural equivalence (which emphasizes ties to exactly the same other actors) to a more general and fuzzier idea that two actors are equivalent if they are similarly embedded.
- Fit of automorphic equivalence models to Knoke information network
-
- But, since automorphic equivalence emphasizes the similarity in the profile of distances of actors from others, the idea of approximate equivalence can be applied to valued data.
- The algorithm scores actors who have similar distance profiles as more automorphically equivalent.
- Again, dimensional scaling or clustering of the distances can be used to identify sets of approximately automorphically equivalent actors.
- Then the reciprocal of the distance is taken, and a vector of the rows entries concatenated with the column entries for each actor is produced.
- Automorphic equivalence of geodesic distances in the line network.
-
- Cluster analysis is a natural method for exploring structural equivalence.
- Network>Roles & Positions>Structural>Profile can perform a variety of kinds of cluster analysis for assessing structural equivalence.
- For directed data, the algorithm will, by default, calculate similarities on the rows (out-ties) but not in-ties.
- There are no exact structural equivalences in the example data.
- Profile similarity of geodesic distances of rows and columns of Knoke information network
-
- Each row of this actor-by-actor correlation matrix is then extracted, and correlated with each other row.
- The block model and its image also provide a description of what it means when we say "the actors in block one are approximately structurally equivalent."
- Actors in equivalence class one are likely to send ties to all actors in block two, but no other block.
- Actors in equivalence class one are likely to receive ties from all actors in blocks 2 and 3.
- So, we have not only identified the classes, we've also described the form of the relations that makes the cases equivalent.
-
- In chemistry, periodic trends are the tendencies of certain elemental characteristics to increase or decrease as one progresses along a row or column of the periodic table of elements.
- Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius.
- Radii generally decrease from left to right along each period (row) of the table, from the alkali metals to the noble gases; radii increase down each group (column).
- As the atomic number increases along a row of the periodic table, additional electrons are added to the same, outermost shell.
- Therefore, the additional electron of next alkali metal (one row down on the periodic table) will go into a new outer shell, accounting for the sudden increase in the atomic radius.
-
- Using elementary operations, Gaussian elimination reduces matrices to row echelon form.
- By means of a finite sequence of elementary row operations, called Gaussian elimination, any matrix can be transformed to a row echelon form.
- Use elementary row operations to reduce the matrix to reduced row echelon form:
- Using elementary row operations to obtain reduced row echelon form ('rref' in the calculator) the solution to the system is revealed in the last column: $x=2, y=3, z=-1$.
- Use elementary row operations to put a matrix in simplified form