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How do you multiply a upper triangular matrix?
Consider the product C=(Cij) of two upper triangular matrices A=(aij) and B=(bij), with n=m (rows=columns). Deduce the expression of C=(Cij).
What is the product of upper and lower triangular matrix?
The transpose of an upper triangular matrix is lower triangular, and vice versa. . The product of two upper triangular matrices is upper triangular. The product of two lower triangular matrices is lower triangular.
Can a matrix be upper and lower triangular?
A matrix that is both upper and lower triangular is diagonal. Matrices that are similar to triangular matrices are called triangularisable. A non-square (or sometimes any) matrix with zeros above (below) the diagonal is called a lower (upper) trapezoidal matrix. The non-zero entries form the shape of a trapezoid.
Is a matrix A upper triangular zero?
A zero square matrix is lower triangular, upper triangular, and also diagonal. Provided it is a square matrix. An upper triangular matrix is one in which all entries below the main diagonal are zero.
What happens if you multiply two upper triangular matrices?
If we multiply two upper triangular, it will result in an upper triangular matrix itself. The inverse of the upper triangular matrix remains upper triangular.
Which is an example of a lower triangular matrix?
An upper triangular matrix is also called right triangular matrix and it is denoted with the letter U. Lower triangular matrices are square matrices whose entries above the main diagonal are zero. Example of a 3×3 dimension lower triangular matrix: A lower triangular matrix is also called left triangular matrix and it is denoted with the letter L.
Is the transpose of a lower triangular matrix invertible?
The transpose of an upper triangular matrix is a lower triangular matrix, and vice versa: the transpose of a lower triangular matrix is an upper triangular matrix. An upper or lower triangular matrix is invertible if all its elements on the main diagonal are nonzero.
Can a square matrix be a triangular matrix?
Any square matrix can be factored into the product of a lower triangular matrix and an upper triangular matrix. That is, any matrix can be transformed into a multiplication of triangular matrices. Also, if the matrix is invertible, this transformation is unique.