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AMM #1
| Question | Answer |
|---|---|
| What is a row and column | . . . . . . . . row . . . . column |
| How to do following operations with vectors 1, scalar multiplication 2, addition 3, subtraction | 1, multiplying all the vector elements with multiplicator 2, additing the same levels of the both vectors 3, negative addition of the same levels of both vectors |
| How do we ad/subtract vectors of different levels | the result is not defined (addition/subtraction only of same dimesion vectors ) |
| What is inner/scalar product of two vectors | v´w = ∑v(i)*w(i) result is one number and the rule is basically as with matrices multiplication |
| What does 1, transpose vector 2,orthogonality mean | 1, transpose vector v´ is in a row instead of column 2, orthogonality of 2 vectors= their scalar product is 0 |
| What is dimension of B Matrix (1 2 3) (4 5 6) | 2x3 Matrix |
| What is a12 & a21 of B Matrix (1 2 3) (4 5 6) | a12 = 2 a21= 4 (1 2 3) (4 5 6) |
| How do we multiplicate matrices | next matrix row = scalar product of row of first matrix with the column of the second matrix |
| What is 1, dimesionality 2,conformity | 1,dimensionality if A = n*m & B=m*p then after multiplication the dimensions are gonna be n*p 2,conformity if A = n*m & B=m*p then m on right (first matrix) and on left (second matrix) mean we can multiply them |
| What is associative law when multiplying matrices | associative law .. it doesnt mater what we multiply first if ranking stays (A*B)*C = A*(B*C) |
| What is distributive law | (A+B)C= AC + AB A(B+C)=AB + AC just as with ordinary numbers |
| How to calculate power of matrices | A^n= A*A*A ...*A exept A^0= I (identity matrix) |
| What is Kronecker Product | written A⊗B A⊗B= (a11*B , a12*B) (a21*B, a22*B) |
| What are the new dimension of Kronecker Product | A = m x n & B=p x q then A⊗B= mp x nq |
| What is. idempodent matrix | idempodent matrix satisfies A^2=A |
| What is trace of a matrix | the sum of all diagonal elements tr(A)=∑a(i,i) |
| What is inverse matrix (2) | 1, A^-1 >> if AxA^(-1)= I (identity matrix) 2,if inverse matrix exist = regular/non-singular if no inverse matrix exist = singular |
| What is 1, (AB)^-1 2,(A´)^-1 | 1, (AB)^-1 = B^-1 x A^-1 2,(A´)^-1 = (A^-1)´ |
| What does determinant says about inverse matrix | if det(A)=0 it is singular otherwise it has a inverse matrix |
Created by:
semester1.IBWL