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A variant of Gaussian elimination called Gauss–Jordan elimination can be used for finding the inverse of a matrix, if it exists. If A is an n × n square matrix, then one can use row reduction to compute its inverse matrix, if it exists. First, the n × n identity matrix is augmented to the right of A, forming an n × 2n block matrix [A | I].
In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) = of certain algebraic groups = into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices—but with exceptional cases.
TI-83 Plus Silver Edition: Zilog Z80 @ 6 MHz/15 MHz (Dual Speed) 128 KB of RAM (24 KB user accessible), 2 MB of Flash ROM (1.5 MB user accessible) 96×64 pixels 16×8 characters 7.3 × 3.5 × 1.0 [4] No 2001 129.95 Allowed Allowed TI-83 Premium CE, TI-83 Premium CE Edition Python: Zilog eZ80 @ 48 MHz
The TI-83 was the first calculator in the TI series to have built-in assembly language support. The TI-92, TI-85, and TI-82 were capable of running assembly language programs, but only after sending a specially constructed (hacked) memory backup. The support on the TI-83 could be accessed through a hidden feature of the calculator.
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The Schur complement arises when performing a block Gaussian elimination on the matrix M.In order to eliminate the elements below the block diagonal, one multiplies the matrix M by a block lower triangular matrix on the right as follows: = [] [] [] = [], where I p denotes a p×p identity matrix.
The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations used to obtain it. The variant of Gaussian elimination that transforms a matrix to reduced row echelon form is sometimes called Gauss–Jordan elimination. A matrix is in column echelon form if its transpose is in row echelon form.
This real Jordan form is a consequence of the complex Jordan form. For a real matrix the nonreal eigenvectors and generalized eigenvectors can always be chosen to form complex conjugate pairs. Taking the real and imaginary part (linear combination of the vector and its conjugate), the matrix has this form with respect to the new basis.