if a and b are invertible matrices?
267575
If A and B are matrices of the same order and are invertible, then (AB)-1 = B-1 A-1.
1064275
['B+C=A.', 'M⋅GCD(B,C) + N⋅GCD(B,C) = A.', '(M + N)⋅GCD(B,C) = A.']
1225499
The eigenvectors of a symmetric matrix A corresponding to different eigenvalues are orthogonal to each other.
535199
According to the definition, the each element in a vector spaces is a vector. So, 2×2 matrix cannot be element in a vector space since it is not even a vector.
78952
A Hermitian (or symmetric) matrix is positive definite iff all its eigenvalues are positive. ... The matrix inverse of a positive definite matrix is also positive definite. The definition of positive definiteness is equivalent to the requirement that the determinants associated with all upper-left submatrices are positive.
1099123
Not necessarily. Semidefinite means that the matrix can have zero eigenvalues which if it does, makes it not invertible. ... Additionally, every vector in the space is a linear combination of the vectors so a similar calculation shows that for every non-zero which would make positive definite.
823799
The bisector of ∠BAC and ∠CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF||BD.
576106
We need to prove that if A and B are invertible square matrices then B-1A-1 is the inverse of AB. Let us denote B-1A-1 by C (we always have to denote the things we are working with). Then by definition of the inverse we need to show that (AB)C=C(AB)=I.
1360499
A symmetric matrix is invertible if it is not singular ( determinant is not equal to 0 ).
655202
Adding and Subtracting Matrices. A matrix can only be added to (or subtracted from) another matrix if the two matrices have the same dimensions . To add two matrices, just add the corresponding entries, and place this sum in the corresponding position in the matrix which results.
367760
No. For instance, the zero matrix is diagonalizable, but isn't invertible. A square matrix is invertible if an only if its kernel is 0, and an element of the kernel is the same thing as an eigenvector with eigenvalue 0, since it is mapped to 0 times itself, which is 0.
71792
is a diagonal matrix with diagonal entries equal to the eigenvalues of A. The position of the vectors Cj in P is identical to the position of the associated eigenvalue on the diagonal of D. This identity implies that A is similar to D. Therefore, A is diagonalizable.
1278081
['Notice that Matrix A is in cells B2:D4.', 'b) We find the inverse of matrix A by Highlighting the cells where you want to place the.', '= MINVERSE(B2:D4)', 'd) When the formula is entered, press the Ctrl key and the Shift key simultaneously, then.', 'press the Enter key.']
81830
Yes they are one and the same. hence (a-b)^2 & (b-a)^2 are same.
1382829
For left inverse of the 2x3 matrix, the product of them will be equal to 3x3 identity matrix. ... If a matrix is invertible that means the inverse is unique, but since the question not saying this 2x3 matrix is invertible, I can't stop thinking that those inverses might be exist.
674484
In general, a square matrix over a commutative ring is invertible if and only if its determinant is a unit in that ring. A has full rank; that is, rank A = n.
848797
If you look up "matrix norms", you'll find lots of material. And if ‖‖ is any matrix norm, then ‖A−B‖ gives you a measure of the "distance" between two matrices A and B. Or, you could simply count the number of positions where |aij−bij| is larger than some threshold number.