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I have a 2x2 matrix "A" which each element is a 12th order polynomial in a parameter "a". I need to raise this matrix "A" to the -t/T power, where T is a known scalar (for this instance it can be assumed T=1) and t is a variable.

I have tried simply

MatrixPower[ A, -t/T] 

but the program ran for over 40 minutes without finishing. This seems unusually long.

Is there a more efficient way of performing this calculation?

EDIT: Here is my matrix in input form.

{ {1.60938*10^-24 a^12 - 8.90757*10^-22 a^11 + 4.1103*10^-19 a^10 - 1.56167*10^-16 a^9 + 4.77859*10^-14 a^8 - 1.1468*10^-11 a^7 + 2.08694*10^-9 a^6 - 2.7542*10^-7 a^5 + 0.0000247781 a^4 - 0.00138637 a^3 + 0.0414932 a^2 - 0.493382 a + 0.898765, 6.40651*10^-26 a^12 - 3.88845*10^-23 a^11 + 1.96554*10^-20 a^10 - 8.25818*10^-18 a^9 + 2.82714*10^-15 a^8 - 7.70067*10^-13 a^7 + 1.62035*10^-10 a^6 - 2.53518*10^-8 a^5 + 2.80165*10^-6 a^4 - 0.000203325 a^3 + 0.00867045 a^2 - 0.179515 a + 1.19691}, {-6.40651*10^-26 a^13 + 3.86315*10^-23 a^12 - 1.95024*10^-20 a^11 + 8.18108*10^-18 a^10 - 2.79488*10^-15 a^9 + 7.5908*10^-13 a^8 - 1.59064*10^-10 a^7 + 2.47333*10^-8 a^6 - 2.70645*10^-6 a^5 + 0.000193079 a^4 - 0.00796119 a^3 + 0.152113 a^2 - 0.765055 a - 0.160599, 1.60938*10^-24 a^12 - 8.90756*10^-22 a^11 + 4.1103*10^-19 a^10 - 1.56167*10^-16 a^9 + 4.77859*10^-14 a^8 - 1.1468*10^-11 a^7 + 2.08694*10^-9 a^6 - 2.7542*10^-7 a^5 + 0.0000247781 a^4 - 0.00138637 a^3 + 0.0414932 a^2 - 0.493382 a + 0.898765} } 

I have a $2 \times 2$ matrix $A$, where each element is a 12th order polynomial in a parameter $a$.

I need to raise this matrix $A$ to the $-t/T$ power, where $T$ is a known scalar (for this instance, it can be assumed $T=1$) and $t$ is a variable.

I have tried simply

MatrixPower[A, -t/T] 

but the program ran for over 40 minutes without finishing. This seems unusually long.

Is there a more efficient way of performing this calculation?

Here is my matrix in input form.

A = { {1.60938*10^-24 a^12 - 8.90757*10^-22 a^11 + 4.1103*10^-19 a^10 - 1.56167*10^-16 a^9 + 4.77859*10^-14 a^8 - 1.1468*10^-11 a^7 + 2.08694*10^-9 a^6 - 2.7542*10^-7 a^5 + 0.0000247781 a^4 - 0.00138637 a^3 + 0.0414932 a^2 - 0.493382 a + 0.898765, 6.40651*10^-26 a^12 - 3.88845*10^-23 a^11 + 1.96554*10^-20 a^10 - 8.25818*10^-18 a^9 + 2.82714*10^-15 a^8 - 7.70067*10^-13 a^7 + 1.62035*10^-10 a^6 - 2.53518*10^-8 a^5 + 2.80165*10^-6 a^4 - 0.000203325 a^3 + 0.00867045 a^2 - 0.179515 a + 1.19691}, {-6.40651*10^-26 a^13 + 3.86315*10^-23 a^12 - 1.95024*10^-20 a^11 + 8.18108*10^-18 a^10 - 2.79488*10^-15 a^9 + 7.5908*10^-13 a^8 - 1.59064*10^-10 a^7 + 2.47333*10^-8 a^6 - 2.70645*10^-6 a^5 + 0.000193079 a^4 - 0.00796119 a^3 + 0.152113 a^2 - 0.765055 a - 0.160599, 1.60938*10^-24 a^12 - 8.90756*10^-22 a^11 + 4.1103*10^-19 a^10 - 1.56167*10^-16 a^9 + 4.77859*10^-14 a^8 - 1.1468*10^-11 a^7 + 2.08694*10^-9 a^6 - 2.7542*10^-7 a^5 + 0.0000247781 a^4 - 0.00138637 a^3 + 0.0414932 a^2 - 0.493382 a + 0.898765} }; 

({ {1.6093810^-24 a^12 - 8.9075710^-22 a^11 + 4.110310^-19 a^10 - 1.5616710^-16 a^9 + 4.7785910^-14 a^8 - 1.146810^-11 a^7 + 2.0869410^-9 a^6 - 2.754210^-7 a^5 + 0.0000247781 a^4 - 0.00138637 a^3 + 0.0414932 a^2 - 0.493382 a + 0.898765, 6.4065110^-26 a^12 - 3.8884510^-23 a^11 + 1.9655410^-20 a^10 - 8.2581810^-18 a^9 + 2.8271410^-15 a^8 - 7.7006710^-13 a^7 + 1.6203510^-10 a^6 - 2.5351810^-8 a^5 + 2.8016510^-6 a^4 - 0.000203325 a^3 + 0.00867045 a^2 - 0.179515 a + 1.19691}, {-6.4065110^-26 a^13 + 3.8631510^-23 a^12 - 1.9502410^-20 a^11 + 8.1810810^-18 a^10 - 2.7948810^-15 a^9 + 7.590810^-13 a^8 - 1.5906410^-10 a^7 + 2.4733310^-8 a^6 - 2.7064510^-6 a^5 + 0.000193079 a^4 - 0.00796119 a^3 + 0.152113 a^2 - 0.765055 a - 0.160599, 1.6093810^-24 a^12 - 8.9075610^-22 a^11 + 4.110310^-19 a^10 - 1.5616710^-16 a^9 + 4.7785910^-14 a^8 - 1.146810^-11 a^7 + 2.0869410^-9 a^6 - 2.754210^-7 a^5 + 0.0000247781 a^4 - 0.00138637 a^3 + 0.0414932 a^2 - 0.493382 a + 0.898765} })

{ {1.60938*10^-24 a^12 - 8.90757*10^-22 a^11 + 4.1103*10^-19 a^10 - 1.56167*10^-16 a^9 + 4.77859*10^-14 a^8 - 1.1468*10^-11 a^7 + 2.08694*10^-9 a^6 - 2.7542*10^-7 a^5 + 0.0000247781 a^4 - 0.00138637 a^3 + 0.0414932 a^2 - 0.493382 a + 0.898765, 6.40651*10^-26 a^12 - 3.88845*10^-23 a^11 + 1.96554*10^-20 a^10 - 8.25818*10^-18 a^9 + 2.82714*10^-15 a^8 - 7.70067*10^-13 a^7 + 1.62035*10^-10 a^6 - 2.53518*10^-8 a^5 + 2.80165*10^-6 a^4 - 0.000203325 a^3 + 0.00867045 a^2 - 0.179515 a + 1.19691}, {-6.40651*10^-26 a^13 + 3.86315*10^-23 a^12 - 1.95024*10^-20 a^11 + 8.18108*10^-18 a^10 - 2.79488*10^-15 a^9 + 7.5908*10^-13 a^8 - 1.59064*10^-10 a^7 + 2.47333*10^-8 a^6 - 2.70645*10^-6 a^5 + 0.000193079 a^4 - 0.00796119 a^3 + 0.152113 a^2 - 0.765055 a - 0.160599, 1.60938*10^-24 a^12 - 8.90756*10^-22 a^11 + 4.1103*10^-19 a^10 - 1.56167*10^-16 a^9 + 4.77859*10^-14 a^8 - 1.1468*10^-11 a^7 + 2.08694*10^-9 a^6 - 2.7542*10^-7 a^5 + 0.0000247781 a^4 - 0.00138637 a^3 + 0.0414932 a^2 - 0.493382 a + 0.898765} } 

I have a 2x2 matrix "A" which each element is a 12th order polynomial in a parameter "a". I need to raise this matrix "A" to the -t/T power, where T is a known scalar (for this instance it can be assumed T=1) and t is a variable.

I have tried simply

MatrixPower[ A, -t/T] 

but the program ran for over 40 minutes without finishing. This seems unusually long.

Is there a more efficient way of performing this calculation?

I have a 2x2 matrix "A" which each element is a 12th order polynomial in a parameter "a". I need to raise this matrix "A" to the -t/T power, where T is a known scalar (for this instance it can be assumed T=1) and t is a variable.

I have tried simply

MatrixPower[ A, -t/T] 

but the program ran for over 40 minutes without finishing. This seems unusually long.

Is there a more efficient way of performing this calculation?

EDIT: Here is my matrix in input form.

({ {1.6093810^-24 a^12 - 8.9075710^-22 a^11 + 4.110310^-19 a^10 - 1.5616710^-16 a^9 + 4.7785910^-14 a^8 - 1.146810^-11 a^7 + 2.0869410^-9 a^6 - 2.754210^-7 a^5 + 0.0000247781 a^4 - 0.00138637 a^3 + 0.0414932 a^2 - 0.493382 a + 0.898765, 6.4065110^-26 a^12 - 3.8884510^-23 a^11 + 1.9655410^-20 a^10 - 8.2581810^-18 a^9 + 2.8271410^-15 a^8 - 7.7006710^-13 a^7 + 1.6203510^-10 a^6 - 2.5351810^-8 a^5 + 2.8016510^-6 a^4 - 0.000203325 a^3 + 0.00867045 a^2 - 0.179515 a + 1.19691}, {-6.4065110^-26 a^13 + 3.8631510^-23 a^12 - 1.9502410^-20 a^11 + 8.1810810^-18 a^10 - 2.7948810^-15 a^9 + 7.590810^-13 a^8 - 1.5906410^-10 a^7 + 2.4733310^-8 a^6 - 2.7064510^-6 a^5 + 0.000193079 a^4 - 0.00796119 a^3 + 0.152113 a^2 - 0.765055 a - 0.160599, 1.6093810^-24 a^12 - 8.9075610^-22 a^11 + 4.110310^-19 a^10 - 1.5616710^-16 a^9 + 4.7785910^-14 a^8 - 1.146810^-11 a^7 + 2.0869410^-9 a^6 - 2.754210^-7 a^5 + 0.0000247781 a^4 - 0.00138637 a^3 + 0.0414932 a^2 - 0.493382 a + 0.898765} })