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Define inverse of matrix

Updated: 11/3/2022
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13y ago

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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.

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13y ago
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Q: Define inverse of matrix
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What is leontief inverse matrix?

(I-A)-1 is the Leontief inverse matrix of matrix A (nxn; non-singular).


Is Inverse of the inverse matrix the original matrix?

Let A by an nxn non-singular matrix, then A-1 is the inverse of A. Now (A-1 )-1 =A So the answer is yes.


How are the inverse matrix and identity matrix related?

If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.


Does every square matrix have an inverse?

No. A square matrix has an inverse if and only if its determinant is nonzero.


What are the applications of det of a matrix?

it is used to find the inverse of the matrix. inverse(A)= (adj A)/ mod det A


How do you find a variable in a matrix if there is no inverse?

The fact that the matrix does not have an inverse does not necessarily mean that none of the variables can be found.


How do you call a matrix that if you multiplied it by the original matrix you would get the identity matrix?

That is called an inverse matrix


Which matrix has no multiplicative inverse?

A rectangular (non-square) matrix.


How to find the inverse of a symmetric matrix?

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.


How to find the inverse of a square matrix?

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.


How to find the Inverse of a square symmetric matrix?

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.


Inverse of 2x1 matrix?

it doesnt have an inverse since only square matrices have an inverse