For example, if we wanted to calculate the determinant of this 3X3 matrix right here, we would have to do 2 multiplied by the 2X2 matrix determinant that you get when you cover up the row and

A determinant of a transformation matrix is essentially a scaling factor for area as you map from one region to another region, or as we go from one region to the image of that region under the transformation. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.
A matrix for which the transposed form is equal to the negative of the original matrix is called a skew-symmetric matrix. Any matrix can be expresses as a sum of a symmetric and a skew-symmetric matrix. For a square matrix A, A = (1/2)(A + A T) + (1/2)(A - A T). If the order of a skew-symmetric matrix is odd, then its determinant is equal to zero.
The outlined squares are known as "Jordan blocks". Each Jordan block contains one number lambda on its main diagonal, and ones above the main diagonal. The lambdas are the eigenvalues of the matrix; they need not be distinct. In linear algebra, a Jordan normal form, also known as a Jordan canonical form ( JCF ), [1] [2] is an upper triangular
If the two roots of a characteristic equation for a 3 × 3 matrix A is 2 + 3i and 2, then the determinant of A is: Q3. If the determinant of the matrix A = \(\left(\begin{array}{ccc}4 & 2 & 6 \\ 5 & 15 & 5 \\ 3 & x & 9\end{array}\right)\) and the determinant of matrix B = \(\left(\begin{array}{ccc}1 & 3 & 1 \\ 1 & y & 3 \\ 2 & 1 & 3\end{array
In this video I will show you a short and effective way of finding the determinant without using cofactors. This method is easy to understand and for most ma
An orthogonal matrix Q is necessarily invertible (with inverse Q−1 = QT ), unitary ( Q−1 = Q∗ ), where Q∗ is the Hermitian adjoint ( conjugate transpose) of Q, and therefore normal ( Q∗Q = QQ∗) over the real numbers. The determinant of any orthogonal matrix is either +1 or −1. As a linear transformation, an orthogonal matrix
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