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Lindsay K.

what is a diagonal matrix?

nxn, all entries that aren't on the principle diagonal are zero.

if you multiply a constant, k, by a diagonal matrix, what is the result?

still a diagonal matrix, with the entries multiplied by the value of k

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what is the result if you add two diagonal matrices together?

a diagonal matrix with the entries added together

what is the result if you multiply two diagonal matrices together?

a diagonal matrix with it's elements being the product of the two matrices

what is a diagonal matrix transposed?

the exact same matrix

if a diagonal matrix has a zero on it's principle diagonal, can you find an inverse?

no - you'd be diving by zero.

what is the inverse of a diagonal matrix?

a diagonal matrix with each of the original elements inverted (1 over each element)

what is a lower triangular matrix?

an nxn matrix where all of the elements **above** the principle diagonal are zero.

what is an upper triangular matrix?

an nxn matrix where all of the elements **below** the principle diagonal are zero.

what is the form of the resultant matrix if you add two upper triangular matrices?

upper triangular matrix

what is the form of the resultant matrix if you multiply a constant, k, by an upper triangular matrix?

an upper triangular matrix

what is the form of the resultant matrix if you multiply two upper triangular matrices?

an upper triangular matrix

what is the form of the resultant matrix if you transpose an upper triangular matrix?

a lower triangular matrix

what is the form of the resultant matrix if you inverse an upper triangular matrix?

upper triangular matrix

what is a symmetric matrix?

a matrix that is symmetrical about the principle diagonal

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if A is a symmetric matrix, what is A^{T}?

A

If A and B are symmetric matrices, what is (A+B)^{T}?

A + B

If A and B are symmetric matrices, what is (AB)^{T}?

=B^{T}A^{T} = BA

what is an antisymmetric (skew) matrix?

an nxn such that A^{-1} = -A

and all elements on princple diagonal are zero.

what is the general result of (A^{-1})^{-1}?

A

what is the general result of (kA)^{-1}?

(1/k)A^{-1}

what is the general result of (A+B)^{-1}?

a fricken mess

what is the general result of (A^{T})^{-1}?

(A^{-1})^{T}

what is the general result of tr(kA)?

k*tr(A)

what is the general result of tr(A+B)?

tr(A)+tr(B)

what is the general result of tr(A^{T})?

tr(A)

what is the general result of (A+B)C?

= AC + BC

what is the general result of C(A+B)?

CA + CB

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