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hayu601
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Homework Statement
Suppose U and V are unitary matrix, A and B are positive definite,
Does:
UAU-1 < VBV-1
implies A < B
and vice versa?
hayu601 said:Homework Statement
Suppose U and V are unitary matrix, A and B are positive definite,
Does:
UAU-1 < VBV-1
implies A < B
and vice versa?
A matrix transformation is a mathematical operation that involves multiplying a matrix by another matrix or a vector. It is used to transform a set of data or coordinates into a new set of data or coordinates.
A matrix transformation is typically represented by a matrix. The matrix contains the coefficients of the transformation and the original coordinates are represented as a column vector. The resulting coordinates are obtained by multiplying the matrix by the original coordinates vector.
An inequality in matrix form is an expression that compares two matrices or vectors using the symbols <, >, ≤, or ≥. It is used to represent a relationship between two sets of data or coordinates.
Matrix inequality is used in various fields such as economics, data analysis, and optimization problems. For example, in economics, it is used to represent the relationship between the supply and demand of goods and services. In data analysis, it is used to compare different sets of data and identify patterns or trends. In optimization problems, it is used to determine the best solution among a set of possible solutions.
The rules for solving matrix inequalities are the same as solving regular algebraic inequalities. You can add or subtract the same number or matrix from both sides, multiply or divide both sides by the same positive number, and flip the inequality sign when multiplying or dividing by a negative number or matrix. Additionally, when both sides of the inequality are multiplied by a matrix, the order of the inequality may change depending on the properties of the matrix used.