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t
HtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHt ^RIHt ^RIHtHt ]t ] t!^RI"H#t# ^RI$H%t% ^RI&H't'H(t( ]'t)]#t*^R	I+H,t,H-t-H.t.H/t/H0t0H1t1H2t2H3t3H4t4H5t5H6t6H7t7H8t8H9t9H:t:H;t;H<t<H=t=H>t>H?t?H@t@HAtAHBtBHCtCHDtDHEtEHFtFHGtGHHtHHItIHJtJHKtKHLtLHMtMHNtNHOtOHPtP ^R
IQHRtR . RNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'NR(NR)NR*NR+NR,NR-NR.NR/NR0NR1NR2NR3NR4NR5NR6NR7NR8NR9NR:NR;NR<NR=NR>NR?NR@NRANRBNRCNRDNRENRFNRGNRHNRINRJNRKNRLNRMNRNNRONRPNRQNRRNRSNtSRT# )UzwA module that handles matrices.

Includes functions for fast creating matrices like zero, one/eye, random
matrix, etc.
)Ú
ShapeErrorÚNonSquareMatrixError)Ú
MatrixKind)ÚGramSchmidtÚ
casoratianÚdiagÚeyeÚhessianÚjordan_cellÚ
list2numpyÚmatrix2numpyÚmatrix_multiply_elementwiseÚonesÚ
randMatrixÚ	rot_axis1Ú	rot_axis2Ú	rot_axis3Úrot_ccw_axis1Úrot_ccw_axis2Úrot_ccw_axis3Ú
rot_givensÚsymarrayÚ	wronskianÚzeros)ÚMutableDenseMatrix)ÚDeferredVectorÚ
MatrixBase)ÚMutableSparseMatrix)Úbanded)ÚImmutableDenseMatrixÚImmutableSparseMatrix)%ÚMatrixSliceÚBlockDiagMatrixÚBlockMatrixÚFunctionMatrixÚIdentityÚInverseÚMatAddÚMatMulÚMatPowÚ
MatrixExprÚMatrixSymbolÚTraceÚ	TransposeÚ
ZeroMatrixÚ	OneMatrixÚblockcutÚblock_collapseÚmatrix_symbolsÚAdjointÚhadamard_productÚHadamardProductÚHadamardPowerÚDeterminantÚdetÚdiagonalize_vectorÚ
DiagMatrixÚDiagonalMatrixÚ
DiagonalOfÚtraceÚ
DotProductÚkronecker_productÚKroneckerProductÚPermutationMatrixÚMatrixPermuteÚ	MatrixSetÚ	PermanentÚper)Údotprodsimpr   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   ÚMatrixÚMutableMatrixr   r   r   r    ÚImmutableMatrixÚSparseMatrixr!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   N)TÚ__doc__Ú
exceptionsr   r   Úkindr   Údenser   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   Ú
matrixbaser   r   rH   rG   Úsparser   Úsparsetoolsr   Ú	immutabler   r    rI   rJ   Úexpressionsr!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   Ú	utilitiesrF   Ú__all__© ó    ÚU/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/matrices/__init__.pyÚ<module>rY      s  ðñ÷
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 ð"ð
 ð"ð
  +ð"ð
 -8ð"ð
 :Dð"ð ð"ð ð"ð *ð"ð ,;ð"ð =Lð"ð ð"ð ð"ð ð"ð #ð"ð ð"ð ð"ð ð"ð" ð#"ð& ð'"ð& 4ð'"ð* ð+"ð* &ð+"ð. ð/"ð. %ð/"ð. '4ð/"ð. 6Fð/"ð0 ð1"ð0 ð1"ð0 $ð1"ð0 &.ð1"ð0 08ð1"ð0 :Fð1"ð2 ð3"ð2 ð3"ð2 )ð3"ð2 +7ð3"ð2 9Dð3"ð4 ð5"ð4 !ð5"ð4 #3ð5"ð4 5>ð5"ð6 ð7"ð6 *ð7"ð6 ,;ð7"ð6 =Jð7"ð8 
ð9"ð8  ð9"ð8 ".ð9"ð8 0@ð9"ð: ð;"ð: ð;"ð: (ð;"ð: *=ð;"ð< ð="ð< ,ð="ð< .=ð="ð< ?Jð="ð> ð?"ð> ð?"ðB ðC"‚rW   