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phymatter
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if a matrix is invertable can it be singular ?
Matrix invertibility is the property of a square matrix where it can be multiplied by another matrix to produce the identity matrix, which is a square matrix with 1s on the main diagonal and 0s everywhere else. In simpler terms, a matrix is invertible if it has an inverse that can "undo" its operations.
Matrix invertibility is important because it allows us to solve linear systems of equations and perform other mathematical operations such as finding determinants and eigenvalues. It also has applications in various fields such as physics, engineering, and computer graphics.
A matrix is singular if it is not invertible, meaning it does not have an inverse. This happens when the determinant of the matrix is equal to 0. Geometrically, a singular matrix represents a transformation that collapses a space onto a lower-dimensional subspace.
To determine if a matrix is invertible, you can calculate its determinant. If the determinant is not equal to 0, then the matrix is invertible. Alternatively, you can also check if the matrix has full rank, which means that all of its columns or rows are linearly independent.
No, a non-square matrix cannot be invertible. Only square matrices have inverses, and the dimensions of the inverse matrix will be the same as the original matrix. However, there are some special types of non-square matrices, such as the pseudoinverse, that can be used in certain cases to "invert" a non-square matrix.