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- Frobenius_matrix abstract "A Frobenius matrix is a special kind of square matrix from numerical mathematics. A matrix is a Frobenius matrix if it has the following three properties: all entries on the main diagonal are ones the entries below the main diagonal of at most one column are arbitrary every other entry is zeroThe following matrix is an example.Frobenius matrices are invertible. The inverse of a Frobenius matrix is again a Frobenius matrix, equal to the original matrix with changed signs outside the main diagonal. The inverse of the example above is therefore:Frobenius matrices are named after Ferdinand Georg Frobenius. An alternative name for this class of matrices is Gauss transformation, after Carl Friedrich Gauss. They are used in the process of Gaussian elimination to represent the Gaussian transformations.If a matrix is multiplied from the left (left multiplied) with a Frobenius matrix, a linear combination ofthe remaining rows is added to a particular row of the matrix. Multiplication with the inverse matrix subtracts the corresponding linear combination from the given row. This corresponds to one of the elementary operations of Gaussian elimination (besides the operation of transposing the rows and multiplying a row with a scalar multiple).".
- Frobenius_matrix wikiPageID "9576297".
- Frobenius_matrix wikiPageRevisionID "583605841".
- Frobenius_matrix hasPhotoCollection Frobenius_matrix.
- Frobenius_matrix subject Category:Matrices.
- Frobenius_matrix type Abstraction100002137.
- Frobenius_matrix type Arrangement107938773.
- Frobenius_matrix type Array107939382.
- Frobenius_matrix type Group100031264.
- Frobenius_matrix type Matrices.
- Frobenius_matrix type Matrix108267640.
- Frobenius_matrix comment "A Frobenius matrix is a special kind of square matrix from numerical mathematics. A matrix is a Frobenius matrix if it has the following three properties: all entries on the main diagonal are ones the entries below the main diagonal of at most one column are arbitrary every other entry is zeroThe following matrix is an example.Frobenius matrices are invertible.".
- Frobenius_matrix label "Frobenius matrix".
- Frobenius_matrix label "Frobenius-matrix".
- Frobenius_matrix label "Frobeniusmatrix".
- Frobenius_matrix label "Postać Frobeniusa".
- Frobenius_matrix sameAs Frobeniusmatrix.
- Frobenius_matrix sameAs Frobenius-matrix.
- Frobenius_matrix sameAs Postać_Frobeniusa.
- Frobenius_matrix sameAs m.02pkly3.
- Frobenius_matrix sameAs Q1469444.
- Frobenius_matrix sameAs Q1469444.
- Frobenius_matrix sameAs Frobenius_matrix.
- Frobenius_matrix wasDerivedFrom Frobenius_matrix?oldid=583605841.
- Frobenius_matrix isPrimaryTopicOf Frobenius_matrix.