elementary matrix sentence in Hindi
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- One can think of each row operation as the left product by an elementary matrix.
- The elementary matrix for any row operation is obtained by executing the operation on the identity matrix.
- One of the three classes of elementary matrix is involutory, namely the " row-interchange elementary matrix ".
- One of the three classes of elementary matrix is involutory, namely the " row-interchange elementary matrix ".
- Define an " elementary matrix " to be one which is the sum of an identity matrix and a single off-diagonal element ( this is different from the definition used in linear algebra ).
- :To answer my own question, yes it must be possible, since any row operation is equivalent to multiplying an elementary matrix from the left . talk ) 21 : 06, 6 June 2010 ( UTC)
- If " E " is an elementary matrix, as described below, to apply the elementary row operation to a matrix " A ", one multiplies the elementary matrix on the left, " E?" A ".
- If " E " is an elementary matrix, as described below, to apply the elementary row operation to a matrix " A ", one multiplies the elementary matrix on the left, " E?" A ".
- A special case of another class of elementary matrix, that which represents multiplication of a row or column by & minus; 1, is also involutory; it is in fact a trivial example of a signature matrix, all of which are involutory.
- I tried looking for these " other contexts " on WP but have only found that it appears to be a case of simple aesthetic preference of the author; square brackets and parentheses seem to be used fairly interchangably in elementary matrix algebra.
- If " C " is a symmetric conference matrix of order " n " > 1, then not only must " n " be congruent to 2 ( mod 4 ) but also " n " & minus; 1 must be a sum of two square integers; there is a clever proof by elementary matrix theory in van Lint and Seidel.
- The argument for n \ geq 2 is similar to the n = 1 case, only one replaces Tietze moves for the fundamental group presentation by elementary matrix operations for the presentation matrices for H _ n ( X; \ mathbb Z ) ( using the presentation matrices coming from cellular homology . i . e . : one can similarly realize elementary matrix operations by a sequence of addition / removal of cells or suitable homotopies of the attaching maps.
- The argument for n \ geq 2 is similar to the n = 1 case, only one replaces Tietze moves for the fundamental group presentation by elementary matrix operations for the presentation matrices for H _ n ( X; \ mathbb Z ) ( using the presentation matrices coming from cellular homology . i . e . : one can similarly realize elementary matrix operations by a sequence of addition / removal of cells or suitable homotopies of the attaching maps.
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