have the same null space. Because elementary row operations are reversible, row equivalence is an equivalence relation. It is commonly denoted by a tilde...

matrix equivalent are not necessarily row equivalent. This makes matrix equivalence a generalization of row equivalence. The rank property yields an intuitive...

additivity formula Matrix equivalence Matrix congruence Matrix similarity Matrix consimilarity Row equivalence Elementary row operations Householder transformation...

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments...

exactly one subset. Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped...

isotopic to a conjugate of the other. This is again an equivalence relation, with the equivalence classes called main classes, species, or paratopy classes...

the columns of C. It follows from the equivalence ( 1 ) ⇔ ( 5 ) {\displaystyle (1)\Leftrightarrow (5)} that the row rank is equal to the column rank. As...

b = g a g − 1 . {\displaystyle b=gag^{-1}.} This is an equivalence relation whose equivalence classes are called conjugacy classes. In other words, each...

automorphic equivalence, and regular equivalence. There is a hierarchy of the three equivalence concepts: any set of structural equivalences are also automorphic...

monoid of all words in the alphabet of positive integers modulo Knuth equivalence. Its elements can be identified with semistandard Young tableaux. It...

preorder is an equivalence relation. Moreover, a preorder on a set X {\displaystyle X} can equivalently be defined as an equivalence relation on X {\displaystyle...

succeeds in placing three of their marks in a horizontal, vertical, or diagonal row first is the winner. It is a solved game, with a forced draw assuming best...

In mathematics, Green's relations are five equivalence relations that characterise the elements of a semigroup in terms of the principal ideals they generate...

the conditional. Truth tables can be used to prove many other logical equivalences. For example, consider the following truth table: This demonstrates the...

by transposition. It is similar to enharmonic equivalence, octave equivalence, and inversional equivalence. In many musical contexts, transpositionally...

"Dram" equivalence is sometimes still used as a measure of the powder charge power in a cartridge. Today, it is an anachronistic equivalence that represents...

Enharmonic equivalence In music theory, equivalence class is an equality (=) or equivalence between properties of sets (unordered) or twelve-tone rows (ordered...

n-dimensional manifolds M and N is an h-cobordism (the h stands for homotopy equivalence) if the inclusion maps M ↪ W and N ↪ W {\displaystyle M\hookrightarrow...

into account). There are 9,985,920 classes of twelve-tone rows up to equivalence (where two rows are equivalent if one is a transformation of the other)...

begin with zero. More generally, for a class of objects on which an equivalence relation is defined, a canonical form consists in the choice of a specific...

Cartesian product of rows from tables in the join. In other words, it will produce rows which combine each row from the first table with each row from the second...

{\displaystyle [x:y]} for homogeneous coordinates denotes the equivalence class of the row vector. The elements of GL2(R) that act trivially on P1(R) are...

that the row player "beats", − means "is beaten" and O means tie Opponent Row player stone paper scissors well Optimal strategy for the row player stone...

bands were constructed and counted for each equivalence class. Summing completions over the equivalence classes, weighted by class size, gives the total...

defined as their dot product. So the equivalence of the two definitions of the dot product is a part of the equivalence of the classical and the modern formulations...

Nielsen transformation taking one to the other (beware this is not an equivalence relation). If the generating sets have the same size, then it suffices...

Stock market equivalence is granted by the European Union to those countries whose stock markets are deemed to be 'equivalent' to those of the EU countries...

Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical...

the logical biconditional, also known as material biconditional or equivalence or bidirectional implication or biimplication or bientailment, is the...

twelve-tone technique, derivation is the construction of a row through segments. A derived row is a tone row whose entirety of twelve tones is constructed from...