28 Why not write $\sqrt{3}2$? 17 Determinant of rank-one perturbations of (invertible) matrices 13 Insightful proofs for Sherman-Morrison Formula and Matrix Determinant Lemma 12 Is there a function that gives the same result for a number and its reciprocal? 9 Are there any decompositions of a symmetric matrix that allow for the inversion of any submatrix?

### Reputation (5,161)

 +10 Mathematical expression to form a vector from diagonal elements +10 Determinant of rank-one perturbations of (invertible) matrices +10 Given the inverse of a block matrix - Complete problem +10 Can a symmetric matrix always be represented as the sum of a positive-definite and negative-definite matrix?

### Questions (10)

 12 Is the square root of a triangular matrix necessarily triangular? 9 Is every square traceless matrix unitarily similar to a zero-diagonal matrix? 6 Characterizing a real symmetric matrix $A$ as $A = XX^T - YY^T$ 5 $\Delta^d m^n =d! \sum_{k} \left[ m \atop k \right] { {k+n} \brace m + d}(-1)^{m+k}$ Is this a new formula? 4 Jacobi's Rotation has two possibilities, why do they both result in same upper triangular magnitude norm?

### Tags (69)

 191 linear-algebra × 99 18 algorithms × 6 177 matrices × 86 18 block-matrices × 5 34 determinant × 10 16 eigenvalues-eigenvectors × 15 28 notation 14 pseudoinverse × 2 20 numerical-linear-algebra × 7 13 optimization × 8

### Bookmarks (28)

 38 How to compute rational or integer points on elliptic curves 30 When is $1^5 + 2^5 + \ldots + n^5$ a square? 16 What sorts of problems can fractals solve? 16 Reference suggestion: eigenvalues of tridiagonal matrices 15 Determinant of a real skew-symmetric matrix is square of an integer