A square matrix is said to be scalene Matrix if it has all principal diagonal elements equal and remaining all
No.But every square is a parallelogram.
No, not every paralellogram is a square. Both 4 sided quadrilaterals. Every square is a parallelogram.
If it's a rhombus and not a square. I fail to see the difficulty here. Every square is a rhombus, but not every rhombus is a square.
Yes, every square is a rhombus because they are all equilateral quadrilaterals.Every square is a rhombus, but not all rhombuses are squares.
A rectangular (non-square) matrix.
From Wolfram MathWorld: The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A-1 such that AA-1=I where I is the identity matrix.
it doesnt have an inverse since only square matrices have an inverse
A non-square matrix cannot be inverted.
In the context of matrix algebra there are more operations that one can perform on a square matrix. For example you can talk about the inverse of a square matrix (or at least some square matrices) but not for non-square matrices.
Inverse matrices are defined only for square matrices.
The inverse of a non-singular, n*n matrix, A Is another n*n matrix, A' such that A*A' = A'*A =I(n), the n*n identity matrix.Singular square matrices do not have inverses, nor do non-square matrices.
The inverse of a 2x2 matrix:[a b][c d]is given by__1___[d -b]ad - bc [-c a]ad - bc is the determinant of the matrix; if this is 0 the matrix has no inverse.The inverse of a 2x2 matrix is also a 2x2 matrix.The browser used here is not really suitable to give details of the inverse of a general matrix.Non-singular square matrices have inverses and they can always be found. Singular, or non-square matrices do not have a proper inverses but canonical inverses for these do exist.
You can factorize the matrix using LU or LDLT factorization algorithm. inverse of a diagonal matrix (D) is really simple. To find the inverse of L, which is a lower triangular matrix, you can find the answer in this link.www.mcs.csueastbay.edu/~malek/TeX/Triangle.pdfSince (A T )-1 = (A-1 )T for all matrix, you'll just have to find inverse of L and D.
You can factorize the matrix using LU or LDLT factorization algorithm. inverse of a diagonal matrix (D) is really simple. To find the inverse of L, which is a lower triangular matrix, you can find the answer in this link.www.mcs.csueastbay.edu/~malek/TeX/Triangle.pdfSince (A T )-1 = (A-1 )T for all matrix, you'll just have to find inverse of L and D.
there are pseudo inverses for non-square matrices a square matrix has an inverse only if the original matrix has full rank which implies that no vector is annihilated by the matrix as a multiplicative operator
(I-A)-1 is the Leontief inverse matrix of matrix A (nxn; non-singular).