Matrices Lecture Notes

Introduction

• Topic: Matrices
• Importance: Crucial topic for scoring
• Objective: Finding inverse, rank, adjoint

Types of Matrices

1. Square Matrix

• Definition: Rows and columns are equal
• Example:
  • 2x2: [\begin{bmatrix} 2 & 1 \ 3 & -1 \end{bmatrix}]
  • 3x3: [\begin{bmatrix} 1 & 0 & -1 \ 3 & 2 & 1 \ -1 & 3 & 2 \end{bmatrix}]

2. Rectangular Matrix

• Definition: Rows ≠ Columns
• Example: 2x3 matrix

3. Unit or Identity Matrix

• Definition: Diagonally 1, all others 0
• Note: Always square

4. Scalar Matrix

• Definition: Diagonally the same number
• Example: 5I

5. Upper and Lower Triangular Matrix

• Upper Triangular: Below diagonal 0
• Lower Triangular: Above diagonal 0

Transpose of Matrix

• Definition: Converting row into column
• Example:
  • [A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}], [A^T = \begin{bmatrix} 1 & 3 \ 2 & 4 \end{bmatrix}]

Symmetric and Skew Symmetric Matrices

Symmetric Matrix

• Definition: (A^T = A)

Skew Symmetric Matrix

• Definition: (A^T = -A)

Determinant of Matrix

• Definition: Process to find the value of a matrix
• Example:
  • For matrix A, find (det(A))

Additional Information

• GATE Question: Join option will be available for GATE questions
• Time: Some lectures might be at night

Conclusion

• Detail: Next lecture will cover A inverse and methods of adjoint
• Time: Next session will be at 11 PM

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