## Cannot get determinant of matrix

7

I have the following variables

Σ = {{64, 40.8, 80}, {40.8, 289, 238}, {80, 238, 400}};
μ = {{9}, {12}, {15}};
ι = {{1}, {1}, {1}};


And then I define the following matrix:

A = {{Transpose[μ].Inverse[Σ].μ,
Transpose[μ].Inverse[Σ].ι}, {Transpose[μ].Inverse[Σ].ι,
Transpose[ι].Inverse[Σ].ι}};


Which gives me the matrix:

Now when I try to get the determinant of the matrix i get an error:

Any1 know what the problem is?

Det will take the determinant of a symbolic matrix, so you could also use something like Det[A] /. {\[CapitalSigma] -> {{64, 40.8, 80}, {40.8, 289, 238}, {80, 238, 400}}, \[Mu] -> {9, 12, 15}, \[Iota] -> {1, 1, 1}} with A as defined below by Bob Hanlon (https://mathematica.stackexchange.com/a/148259/106) – user1066 – 2017-06-13T14:34:19.483

11

Mathematica does not distinguish between row and column vectors ("The Wolfram Language represents vectors as lists, and never needs to distinguish between row and column cases."). Consequently, change your definitions of μ, ι, and A.

Σ = {{64, 40.8, 80}, {40.8, 289, 238}, {80, 238, 400}};
μ = {9, 12, 15};
ι = {1, 1, 1};

(A = {{μ.Inverse[Σ].μ, μ.Inverse[Σ].ι},
{μ.Inverse[Σ].ι, ι.Inverse[Σ].ι}}) // MatrixForm


Det[A]

0.0021282


5

The problem is the structure of A. You need to use Flatten and First to get rid of the curly around each number.

Σ = {{64, 40.8, 80}, {40.8, 289, 238}, {80, 238, 400}};
μ = {{9}, {12}, {15}};
ι = {{1}, {1}, {1}};

A = {{First@Flatten[Transpose[μ].Inverse[Σ].μ],
First@Flatten[Transpose[μ].Inverse[Σ].ι]}, {First@
Flatten[Transpose[μ].Inverse[Σ].ι],
First@Flatten[Transpose[ι].Inverse[Σ].ι]}};



Det[A]


0.0021282

4

What you have constructed is a four-dimensional array (matrix of matrices).

To contruct a normal two-dimensional matrix from two-dimensional blocks use ArrayFlatten:

A = ArrayFlatten[{{Transpose[μ].Inverse[Σ].μ, Transpose[μ].Inverse[Σ].ι},
{Transpose[μ].Inverse[Σ].ι, Transpose[ι].Inverse[Σ].ι}}];

{{1.41771,  0.151394 },
{0.151394, 0.0176682}}