Linear Algebra28

Non-degenerate form induces adjoint linear operators
Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.9 Solution: We can always de...
Relation between non-degenerate forms and linear functionals
Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.8 Solution: We can always de...
Form is left non-degenerate if and only if it is right non-degenerate
Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.7 Solution: Call the form $f...
Form is non-degenerate if and only if the associated linear operator is non-singular
Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.6 Solution: If $f$ is non-de...
Diagonalize a symmetric matrix associated to a form
Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.5 Solution: The matrix of $f...
Symmetric sesqui-linear form over $\mathbb C$ is zero
Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.4 Solution: Since $f$ is a f...
Check if a form is an inner product
Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.3 Solution: Because $A=A^*$,...
Find the matrix of a form with respect to a basis
Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.2 Solution: It is not a form...
Verify if they are sesqui-linear forms
Solution to Linear Algebra Hoffman & Kunze Chapter 9.2 Exercise 9.2.1 Solution: (a) No. Since $f...
Solve general linear equations with $2\times 2$ matrix
Solution to Linear Algebra Hoffman & Kunze Chapter 1.3 Exercise 1.3.8 Solution: (a) In this case...