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- Involutory_matrix abstract "In mathematics, an involutory matrix is a matrix that is its own inverse. That is, matrix A is an involution if and only if A2 = I.One of the three classes of elementary matrix is involutory, namely the row-interchange elementary matrix. A special case of another class of elementary matrix, that which represents multiplication of a row or column by −1, is also involutory; it is in fact a trivial example of a signature matrix, all of which are involutory.Involutory matrices are all square roots of the identity matrix. This is simply a consequence of the fact that any nonsingular matrix multiplied by its inverse is the identity. If A is an n × n matrix, then A is involutory if and only if ½(A + I) is idempotent.An involutory matrix which is also symmetric is an orthogonal matrix, and thus represents an isometry (a linear transformation which preserves Euclidean distance). A reflection matrix is an example of an involutory matrix.Clearly, any block-diagonal matrices constructed from involutory matrices will also be involutory, as a consequence of the linear independence of the blocks.".
- Involutory_matrix wikiPageID "7917643".
- Involutory_matrix wikiPageRevisionID "560870441".
- Involutory_matrix hasPhotoCollection Involutory_matrix.
- Involutory_matrix subject Category:Matrices.
- Involutory_matrix type Abstraction100002137.
- Involutory_matrix type Arrangement107938773.
- Involutory_matrix type Array107939382.
- Involutory_matrix type Group100031264.
- Involutory_matrix type Matrices.
- Involutory_matrix type Matrix108267640.
- Involutory_matrix comment "In mathematics, an involutory matrix is a matrix that is its own inverse. That is, matrix A is an involution if and only if A2 = I.One of the three classes of elementary matrix is involutory, namely the row-interchange elementary matrix.".
- Involutory_matrix label "Involutory matrix".
- Involutory_matrix label "Matrice involutoria".
- Involutory_matrix label "Matriz involutiva".
- Involutory_matrix label "Инволютивная матрица".
- Involutory_matrix sameAs Matriz_involutiva.
- Involutory_matrix sameAs Matrice_involutoria.
- Involutory_matrix sameAs m.026j_w2.
- Involutory_matrix sameAs Q1052516.
- Involutory_matrix sameAs Q1052516.
- Involutory_matrix sameAs Involutory_matrix.
- Involutory_matrix wasDerivedFrom Involutory_matrix?oldid=560870441.
- Involutory_matrix isPrimaryTopicOf Involutory_matrix.