Matrix & Vector calculators

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Matrix & Vector Calculators (examples)

1.1 Matrix operations
1. Addition/Subtraction of two matrix
2. Multiplication of two matrix
3. Division of two matrix
4. Power of a matrix
5. Transpose of a matrix
6. Determinant of a matrix
7. Adjoint of a matrix
8. Inverse of a matrix
9. Prove that any two matrix expression is equal or not
10. Minor of a matrix
11. Cofactor of a matrix
12. Trace of a matrix

1.2 Matrix operations
1. Transforming matrix to Row Echelon Form
2. Transforming matrix to Reduced Row Echelon Form
3. Rank of matrix
4. Characteristic polynomial
5. Eigenvalues
6. Eigenvectors
7. Triangular Matrix
8. LU Decomposition using Gauss Elimination method
9. LU decomposition using Doolittle's method
10. LU decomposition using Crout's method
11. Diagonal Matrix
12. Cholesky Decomposition
13. QR Decomposition (Gram Schmidt Method)
14. QR Decomposition (Householder Method)
15. LQ Decomposition
16. Pivots of a Matrix
17. SVD - Singular Value Decomposition
18. Moore-Penrose Pseudoinverse of a Matrix
19. Power Method for dominant eigenvalue
20. Determinants using Sarrus Rule
21. Determinants using properties of determinants
22. Row Space
23. Column Space
24. Null Space

1.3 Matrix Structure
0. Auto Detect the matrix type
1. is Row Matrix
2. is Column Matrix
3. is Square Matrix
4. is Horizontal Matrix
5. is Vertical Matrix
6. is Diagonal Matrix
7. is Identity Matrix
8. is Scalar Matrix
9. is Null Matrix
10. is Lower Triangle Matrix
11. is Upper Triangle Matrix
12. is Orthogonal Matrix
13. is Singular Matrix
14. is Nonsingular Matrix
15. is Symmetric Matrix
16. is Skew Symmetric Matrix
17. is Nilpotent Matrix
18. is Involutary Matrix
19. is Idempotent Matrix
20. is Periodic Matrix
21. is Positive Definite Matrix
22. is Negative Definite Matrix
23. is Derogatory Matrix
24. is Diagonally Dominant Matrix
25. is Strictly Diagonally Dominant Matrix

2. Find inverse of a matrix using
1. Adjoint method
2. Gauss-Jordan Elimination method
3. Cayley Hamilton method method

3. Solve linear equation of any number of variables using
1. Inverse Matrix method
2. Cramer's Rule method
3. Gauss-Jordan Elimination method
4. Gauss Elimination Back Substitution method
5. Gauss Seidel method
6. Gauss Jacobi method
7. Elimination method
8. LU decomposition using Gauss Elimination method
9. LU decomposition using Doolittle's method
10. LU decomposition using Crout's method
11. Cholesky decomposition method
12. SOR (Successive over-relaxation) method
13. Relaxation method

4. Vector Algebra
1. Addition/Subtraction of two vectors
2. Scalar Multiplication of vectors
3. Dot Product of two vectors
4. Cross Product of two vectors
5. Magnitude(length) of a vector
6. Unit vector
7. Direction cosines of a vector
8. Component form of a vector given two points
9. Angle between two vectors
10. Vector projections of B onto A
11. Orthogonal vectors
12. Collinear vectors
13. Coplanar vectors
14. Scalar triple product
15. Vector triple product
16. Area of triangle determined by two vectors
17. Area of parallelogram determined by two vectors
18. Volume of pyramid determined by vectors
19. Volume of Parallelepiped determined by vectors
20. Decomposition of vector in basis
21. Linearly dependent and linearly independent vectors

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