No, it does not.
To square a matrix, simply multiply the matrix by itself. It is just like squaring any other regular number in mathematics.
First, You have to reduce the matrix to echelon form . The number of nonzero rows in the reduced echelon form matrix (number of linearly independent rows) indicates the rank of the matrix. Go to any search engine and type "Rank of a matrix, Cliffnotes" for an example.
Rank of a matrix is used to find consistency of linear system of equations.As we know most of the engineering problems land up with the problem of finding solution of a linear system of equations ,at that point rank of matrix is useful.
The statement that the rank of product of two matrices cannot exceed the rank of either factor is a true statement. The rank of a matrix is the largest number of linearly independent rows or columns. The column rank is equal to the row rank in every matrix.
Then it has (not have!) a unique solution.
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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
A null matrix is a matrix with all its elements zero.EXAMPLES : (0 0) is a null row matrix.(0 0)(0 0) is a null square matrix.NOTE : Text handling limitations prevent the printing of large brackets to enclose the matrix array. Two pairs of smaller brackets have therefore been used.Answer 2:The above answer is a null matrix. However, the nullity of a matrix is the dimension of the kernel. Rank + Nullity = Dimension. So if you have a 4x4 matrix with rank of 2, the nullity must be 2. This nullity is the number of "free variables" you have. A 4x4 matrix is 4 simultaneous equations. If it is rank 2, you have only two independent equations and the other two are dependent. To solve a system of equations, you must have n independent equations for n variables. So the nullity tells you how short you are in terms of equations.
A scalar, which is a tensor of rank 0, is just a number, e.g. 6 A vector, which is a tensor of rank 1, is a group of scalars, e.g. [1, 6, 3] A matrix, which is a tensor of rank 2, is a group of vectors, e.g. 1 6 3 9 4 2 0 1 3 A tensor of rank 3 would be a group of matrix and would look like a 3d matrix. A tensor is the general term for all of these, and the generalization into high dimensions.
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