95年 - 95 淡江大學轉學考應用數學#55952

科目：研究所、轉學考(插大)-應用數學 | 年份：95年 | 選擇題數：0 | 申論題數：6

試卷資訊

所屬科目：研究所、轉學考(插大)-應用數學

選擇題 (0)

申論題 (6)

1 (a) Two Hermitian matrices A and B have the same eigenvalues. S now tlial A and B are related by a unitary similarity transformation. (10 points)

(b) Show that llie sum of the square of the matrix elements is mvarianl under orlhogonaJ similarity transformation. (10 points)

2. Wrile down the mathematical expression of convolution associated with two given functions f(t) and g(t) and briefly explain how convolution can be employed in spectroscopy. (20 poinls)

【已刪除】3. Evaluate

and S is Ihe surface of I he hemisphere x² + y² + z² = a² with z≥0, (20 point)

【已刪除】4. Show that ihe Fourier series for the function y(x) = |x| in the range of -π ＜x＜n is

and deduce the suiii of the infinile series

? (20 poinls)

【已刪除】5. Evaluate

(20 poinls)