If
is an
upper triangular matrix, and
is an
lower triangular matrix, then AB^T is an
upper triangular matrix.

Question

If is an upper triangular matrix, and is an lower triangular matrix, then AB^T is an upper triangular matrix.

Quizplus · Accepted Answer

The given string is a sequence of abbreviations representing matrices. 'ABS' represents a matrix that is the absolute value of a given matrix, '1U' represents a matrix that has 1's in the upper triangle and 0's elsewhere, '1P' represents a matrix that has 1's on the main diagonal and 0's elsewhere, '1TS' represents a matrix that is the transpose of a given matrix, and '1S' represents a matrix that is the inverse of a given matrix. '0' represents a matrix of all 0's.

Therefore, starting with the upper triangular matrix given in the question, applying the absolute value ('ABS'), then a matrix with 1's in the upper triangle and 0's elsewhere ('1U'), results in an upper triangular matrix with absolute values.

If Is an