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TheScienceAlliance
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[MHB thread moved to the PF schoolwork forums by a PF Mentor]
For every square matrix A, C=A(A^t)+(A^t)A is symmetric.
For every square matrix A, C=A(A^t)+(A^t)A is symmetric.
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TheScienceAlliance said:For every square matrix A, C=A(A^t)+(A^t)A is symmetric.
A square matrix is a matrix with the same number of rows and columns. It is represented by a capital letter and its size is denoted by the number of rows/columns. For example, a 3x3 square matrix has 3 rows and 3 columns.
To determine if a matrix is square, you can count the number of rows and columns. If they are equal, then the matrix is square. Alternatively, you can also check the size of the matrix by looking at the number of elements in each row and column. If they are equal, then the matrix is square.
A square matrix has the same number of rows and columns, while a non-square matrix has a different number of rows and columns. Additionally, square matrices have some special properties and operations that can only be applied to them, such as finding the determinant or calculating the inverse.
Yes, a square matrix can have a negative determinant. The determinant is a scalar value that represents the scaling factor of the matrix. It can be positive, negative, or zero. The sign of the determinant does not affect the squareness of the matrix.
The inverse of a square matrix is another matrix that, when multiplied with the original matrix, gives the identity matrix. It is denoted by A-1 and is only defined for square matrices that have a non-zero determinant. The inverse of a matrix can be used to solve systems of linear equations and perform other mathematical operations.