Exam: GRE (Verbal)

Definition: Able to be arranged in a diagonal form, especially in mathematics when referring to matrices that can be transformed into a diagonal matrix.

Example: The matrix is diagonalizable, which simplifies the calculations for its eigenvalues.

Definition: The process of transforming a matrix into a diagonal form, where all non-diagonal elements are zero, often used in linear algebra.

Example: The diagonalization of the matrix made it easier to solve the equations.

Definition: To change a square matrix into a diagonal matrix by using another matrix and its inverse, so that all the nonzero elements are arranged from the upper left to the lower right.

Example: In linear algebra, we often diagonalize matrices to simplify calculations.

Definition: Changed into a form where the elements outside the main diagonal are zero, often used in mathematics and linear algebra.

Example: The matrix was diagonalized to simplify the calculations.

Definition: To change a matrix into a diagonal form, where all the non-diagonal elements are zero, often used in mathematics and linear algebra.

Example: The mathematician diagonalized the matrix to simplify the calculations.

Definition: Relating to or represented in the form of a diagram, which is a visual representation of information or data.

Example: The teacher used a diagrammatic approach to explain the complex concept clearly.

Definition: Relating to or represented in the form of a diagram, which is a simplified drawing showing the appearance, structure, or workings of something.

Example: The teacher used a diagrammatical representation to explain the complex process.

Definition: The last phase of the first stage of cell division where chromosomes become shorter and thicker, and the cell prepares to divide.

Example: During diakinesis, the chromosomes become more visible under a microscope as they condense.

Definition: A way of discussing or thinking about ideas that involves examining opposing viewpoints to find the truth or resolve contradictions.

Example: In philosophy class, we studied dialectic to understand how different ideas can interact and lead to new insights.

Definition: Relating to the method of reasoning that involves the exchange of opposing ideas to arrive at a truth or understanding.

Example: The philosopher used a dialectical approach to explore the complexities of human thought.

Definition: In a way that relates to the method of reasoning or argument that involves contradiction and its reconciliation.

Example: The philosopher argued dialectically, presenting opposing viewpoints to reach a deeper understanding.