By Zhe-xian Wan.
1. Linear Algebra over department earrings --
2. Affine Geometry and Projective Geometry --
3. Geometry of oblong Matrices --
4. Geometry of other Matrices --
5. Geometry of Symmetric Matrices --
6. Geometry of Hermitian Matrices.
Read or Download Geometry of matrices : in memory of Professor L.K. Hua (1910-1985) PDF
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Additional resources for Geometry of matrices : in memory of Professor L.K. Hua (1910-1985)
Example text
Proof: Let A be left invertible. Then there is an n x n matrix B such that BA = I< Then H is cogredient to a diagonal matrix (ai \ I I' \ o Since S is nonalterate, there is a nonzero diagonal element of 5, say s u ^ 0. Interchanging the first row and the i-th row of S and the first column and the i-th column of S simultaneously, we obtain a symmetric matrix which is cogredient to S and whose element at (1, 1) position is nonzero. Therefore we can assume that s u ^ 0. Write 5 = | ( 311 u V 522 / where U u — and5*22 S22= =(St*)2